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ADVANCED  ARITHMETIC 


BY 


DAVID   EUGENE    SMITH,  LL.D. 

Professor  of  Mathematics  in  Teachers  College 
Columbia  University,  New  York 


GINN  &  COMPANY 

BOSTON  •  NEW  YORK  •  CHICAGO  •  LONDON 


\X'  %.  WxyytnM^kl  8,'i'5u..-;^-fe 


Entered  at  Stationers'  Hall 


Copyright,  1904,  1905 
By   DAVID  EUGENE  SMITH 


ALL  RIGHTS   RESERVED 


97.11 


GIXN   &   COMPANY  .  PRO- 
PRIETORS .  BOSTON  .  U.S.A. 


PEEFACE 

The  following  have  been  controlling  ideas  in  the  prepa- 
ration of  this  book : 

1.  In  sequence  of  topics,  to  follow  the  plan  adopted  in 
the  author's  Primary  and  Intermediate  Arithmetics,  that 
of  recognizing  the  value  of  the  various  courses  of  study  in 
use  in  different  parts  of  the  country.  Whatever  originality 
may  be  demanded  and  legitimately  shown  in  the  prepara- 
tion of  a  text-book,  an  author  is  bound  to  recognize  the  con- 
sensus of  opinion  as  to  topics  and  sequence.  For  example, 
modern  courses  invariably  suggest  the  repetition  of  the 
most  important  portions  of  arithmetic  from  time  to  time, 
but  they  favor  a  somewhat  exhaustive  treatment  of  each 
subject  whenever  it  is  under  discussion.  The  extreme  spiral 
system,  in  which  no  topic  is  ever  thoroughly  treated  at  one 
time,  but  each  is  repeated  until  the  pupil  wearies  of  it,  is 
psychologically  too  unwarranted  to  be  considered  seriously. 
On  the  other  hand,  the  old-time  plan  of  presenting  important 
chapters  but  once  is  equally  unscientific.  Between  these 
extremes  lies  the  mean  of  the  modern  courses  of  study. 

2.  In  arrangement  by  grades,  to  recognize  the  prevailing 
courses  of  study  in  the  country,  and  to  outline  the  work 
usually  covered  in  the  seventh  and  eighth  school  years, 
the  author's  Intermediate  Arithmetic  having  covered  the 
work  of  the  fifth  and  sixth  years. 

3.  In  the  selection  of  problems,  to  touch  the  actual  life 
of  this  country  at  this  time  ;  to  give  correct  ideas  of  the 
business  customs  of  to-day ;  to  embody  the  mathematical 
principles  in  interesting  and  instructive  groups  of  problems; 

f)4  46**4 


iv  PREFACE 

to  touch  the  genuine  interests  of  pupils  in  the  story  of 
our  national  resources  and  industries  rather  than  to  dwell 
upon  the  technicalities  of  minor  trades  in  which  they 
have  no  immediate  or  prospective  concern;  and  to  come 
in  contact  with  human  life  rather  than  with  those  phases 
of  science  which  are  quite  as  foreign  to  the  interests  of  boys 
and  girls  as  are  the  mere  abstract  problems  of  numbers. 

4.  In  the  matter  of  abstract  drill  work,  to  recognize  the 
fact  that  a  large  number  of  "problems  without  content'' 
are  necessary  to  concentrate  the  attention  on  the  operations 
and  to  impart  the  computing  habit.  The  numbers  selected 
have  been  those  demanded  by  the  conditions  of  the  present 
day,  the  fractions  and  compound  numbers  being  those  in 
common  use  rather  than  those  never  met  in  business,  and 
the  integers  being  the  ordinary  ones  of  daily  life.  Very 
large  numbers  have  generally  been  used  only  in  such  applied 
problems  as  represent  the  real  conditions  that  the  children 
meet  in  their  geography,  their  elementary  science,  and  their 
newspaper  reading. 

The  necessity  for  a  frequent  review  of  the  fundamental 
operations  is  recognized  by  all  teachers,  and  hence  the  book 
opens  with  such  a  review,  presenting  the  subject  in  a 
slightly  more  scientific  manner  and  introducing  such  short 
processes  as  are  really  usable  in  business. 

In  fine,  the  book  is  written  for  the  use  of  those  teachers 
who  wish 'to  preserve  the  best  that  was  in  the  old-style 
arithmetic,  with  its  topical  system  and  its  abundant  drill, 
while  giving  to  it  a  modern  arrangement  and  securing 
"mental  discipline"  through  problems  of  to-day  rather 
than  through  the  tiresome,  meaningless,  unreal  inherit- 
ances of  the  past. 

DAVID  EUGENE  SMITH 


CONTENTS 


CHAPTER  I 

I.   A  GENERAL  REVIEW  OF  ARITHMETIC 

PAGE 

Writing  Numbers      .         .         .         ...         .         .         .  1 

Addition  Reviewed       ........  8 

Subtraction  Reviewed 12 

Multiplication  Reviewed    .......  16 

Division  Reviewed    .........  20 

General  Principles  of  the  Operations     ....  27 

Practical  Short  Methods .  28 

Measures 47 

II.   MEASURES.    PERCENTAGES.    PROPORTION 

Volumes .67 

Longitude  and  Time     .         .         .         .         ;         .         .         .  75 

Percentage  Reviewed      ........  84 

Simple  Interest  Reviewed           ......  99 

Ratio  and  Proportion  Reviewed    ......  117 

Review  Problems 128 

CHAPTER  II 

I.   BUSINESS  APPLICATIONS 

Going  into  Business 138 

Bank  Accounts 141 

Partial  Payments 164 

Trade  Discount 158 

Simple  Accounts *        .  162 

Partnership 164 

V 


vi  CONTENTS 

PAGE 

Exchange 167 

Metric  System 178 

Taxes          .         .         .         .         .         . 190 

Fire  Insurance •  .    .    .  201 

Marine  Insurance 205 

Life  Insurance   .........  206 


II.  BUSINESS  ARITHMETIC  CONTINUED.    MENSURATION 

Corporations      ..........  210 

Buying  Produce      .........  219 

Industrial  Problems         ........  221 

Powers  and  Roots  .        f        .....         .  230 

Mensuration      ..........  248 

Miscellaneous  Problems       .         .         .         .         .         .         .  266 

Tables  for  Reference      ........  280 

Definitions     ..........  285 

INDEX        ......         o         o         ...  294 


AD YA:^rCED  ARITHMETIC 

CHAPTER   I 

I.    A  GENERAL  REVIEW  OF  ARITHMETIC 
WRITING  NUMBERS 

1.  Reason  for  this  review.  This  class  has  now  studied 
most  of  the  important  subjects  of  Arithmetic.  Soon  we 
shall  take  the  more  advanced  business  applications.  As  an 
aid  to  this  advanced  work  we  should  review  the  founda- 
tions of  all  work  in  Arithmetic,  the  common  operations. 

Where  such  a  review  is  not  thought  to  be  advisable,  it  will  of 
course  be  omitted. 

2.  Origin  of  our  numerals.    Our  numerals,  1,  2,  and  so  on 

to  9,  originated  in  India  about  2000  years  ago.  The  zero  (0) 
was  added  more  than  1200  years  ago,  thus  making  the  sys- 
tem the  excellent  one  that  we  now  know.  Without  the  0  it 
was  but  little  better  than  the  Roman  system.  The  numerals 
were  learned  by  the  Arabs  more  than  1100  years  ago,  and  by 
A.D.  1200  became  somewhat  known  in  Europe.  About  400 
years  ago  they  became  well  known  in  schools  and  in  busi- 
ness, and  they  are  now  used  i*n  most  of  the  civilized  world. 

3.  The  great  feature  of  this  system.  It  is  the  jplace  value 
that  makes  the  Arabic  or  Hindoo  system  better  than  all 
others.  The  Roman  VI  means  five  +  one,  while  51  means 
five  tens  +  one,  the  5  having  not  only  the  value  five^  but  the 
place  value  tens. 

4.  Decimal  system.  Because  the  places  or  orders  increase 
tenfold  to  the  left,  and  decrease  by  tenths  to  the  right,  we 
call  our  system  a  decimal  system^  from  the  Latin  decern, 
meaning  ten. 


;  i  ^  J ; 


WRITING  NUMBERS 


ORAL   EXERCISE 


1.  How  many  different  figures  are  used  in  the  Arabic 
system?  How  many  in  the  Roman  system  for  numbers 
below  a  hundred? 

2.  If  I  write  ten  five  in  figures  in  the  two  systems,  105 
and  Xy,  what  values  are  indicated  ?  Why  do  the  two  num- 
bers have  different  values  ?    What  is  the  use  of  the  0  ? 

3.  In  the  number  1,904,52^,738,  give  the  place  value  of 
each  figure,  as  8  units,  3  tens,  and  so  on.  Give  the  name 
of  each  period,  as  738  units,  526  thousands,  and  so  on. 

4.  What  do  you  mean  by  the  words  separatrix,  order, 
period,  decimal^  naught,  place  value,  billion?  Do  not  try  to 
repeat  definitions,  but  answer  in  your  own  way. 

5.  Why  is  our  common  system,  the  Arabic,  better  than 
the  old  Roman  system  ?  You  might  illustrate  by  trying  to 
multiply  one  number  by  another. 

-     6.    Read  the  following  numbers  taken  from  book  chap- 
ters :  XXVIII,  XLI,  LXI,  LXXXIX,  XCIV,  CLXVI. 

WRITTEN  EXERCISE 

1.  Write  in  the  Arabic  system  :  MDCLXIX,  MCCCXLIY. 

2.  Write  in  the  Roman  system :  49,  79,  94,  96,  99,  146. 

3.  Write  in  the  Roman  system  the  number  of  the  present. 
year ;  of  last  year ;  of  fifty  years  ago. 

4.  Write  in  the  Arabic  system  the  number  twenty-one 
million,  four  hundred  seventy-five. 

5.  Write  in  common  figures  the  number  one  billion,  one 
million,  one  thousand  one,  and  one  ten-thousandth. 

6.  Write  in  common  figures  the  number  of  Ex.  5  decreased 
by  42,675;  also  by  12.245;  also  by  295,001.127. 


SCALES  3 

5.  Uniform  scale.  Because  in  our  system  of  writing  num- 
bers each  place  has  uniformly  ten  times  the  value  of  the 
place  at  its  right,  we  are  said  to  use  a  uniform  scale. 
Because  this  is  a  scale  of  ten  it  is  called  a  decimal  scale, 

6.  Varying  scale.  A  scale  that  is  not  uniform  is  called  a 
varying  scale. 

.  Uniform  Scale  Varying  Scale 

10  units         =  1  ten.  2  pints    =  1  quart. 

10  tens  =  1  hundred.  8  quarts  =  1  peck. 

10  hundreds  =  1  thousand.  4  pecks   =  1  bushel. 


ORAL   EXERCISE 

1.  What  is  an  even  number  ?     Illustrate. 

2.  What  name  is  given  to  numbers  that  are  not  even? 

3.  How  can  you  tell  whether  or  not  a  number  is  even  ? 
^^   4.    What  is  meant  by  the  word  integer  ?  the  word  frac- 
tion? the  exipTession  decimal  system? 

5.  Give  three  illustrations  of  a  varying  scale.  What 
kind  of  scale  is  that  of  United  States  money? 

6.  Tell  some  reasons  why  the  decimal  fraction  is  better 
for  practical  use  than  the  common  fraction,  except  in  a  few 
cases. 

WRITTEN   EXERCISE 

^  1.  Write  in  common  figures  the  number  one  hundred 
forty-two  thousand,  eight  hundred  fifty-seven. 

^ '  2.  Multiply  the  number  in  Ex.  1  by  2,  by  3,  by  4,  by  5, 
and  by  6,  and  write  the  results  in  words. 

The  results  in  Ex.  2  are  peculiar,  all  having  the  same  figures 
as  the  number  multiplied,  but  differently  arranged. 


4  WRITING  NUMBERS 

-^  3.  Count  by  3's  from  3  to  27  and  write  the  results. 
Multiply  37  by  each  of  these  numbers  and  write  the  nine 
products. 

In  Ex.  2  one  of  the  interesting  numbers  of  Arithmetic  was 
considered,  and  another  of  the  curiosities  of  number  is  seen  in 
this  example.  With  a  view  to  further  interest,  several  other  curi- 
.  ous  properties  are  given  in  the  following  examples. 

-^  4.  Count  by  9's  from  9  to  81  and  write  the  results. 
Multiply  12,345,679  by  each  of  these  numbers  and  write 
the  nine  products. 

5.  Multiply  142,857  by  326,451  and  tell  the  peculiari- 
ties of  the  partial  products. 

6.  Multiply  the  following  numbers  by  7:  15,873, 
31,746,  47,619,  63,492,  79,365,  95,238,  111,111,  126,984, 
142,857,  each  number  being  15,873  more  than  its  prede- 
cessor. 

7.  Perform  the  multiplications  indicated :  9x9,  99  x 
99,  999  X  999,  9999  x  9999.  Write  a  rule  for  such  prod- 
ucts, and  apply  it  to  writing  the  product  of  99,999  by 
99,999. 

^—-8.  Perform  the  multiplications  indicated :  11  x  11, 
111  X  111,  1111  X  1111.  Write  a  rule  for  such  products, 
and  apply  it  to  writing  the  product  of  111,111  by  111,111. 
9.  Multiply  143  by  7;  by  11  x  7 ;  by  135  x  7;  by  234  x  7. 
From  these  results  tell  what  the  result  would  be  of  multi- 
plying by  345  X  7  ;  by  789  x  7. 

10.    Write  the  values  of  the  following : 

0x9+1  0x9+8 

1x9+2  9x9+7 

12x9  +  3  98x9  +  6 

123  X  9  +  4  987  X  9  +  5 

1234  X  9  +  5  9876  x  9  +  4 


UNITS  5 

7.  Units.  We  usually  speak  of  things  counted  as  units. 
If  we  are  counting  dollars,  $1  is  the  unit;  if  cents,  1  ct.  is 
the  unit;  if  dozens,  1  doz.  is  the  unit;  if  thousands,  1000* 
is  the  unit.  If  we  are  counting  fifths,  J  is  the  unit,  and  we 
count  1,  f ,  I,  and  so  on.  A  unit  may,  therefore,  be  one 
object,  or  a  group  of  objects,  or  a  part  of  some  object. 

ORAL   EXERCISE 

1.  Count  from  \  to  1,  using  \  as  the  unit. 

2.  Count  from  0.1  to  1,  using  0.1  as  the  unit. 

3.  State  the  most  common  units  of  length  and  tell  where 
we  might  use  each. 

4.  State  the  most  common  units  of  area  and  tell  where 
we  might  use  each. 

5.  State  the  most  common  units  of  capacity  (and  volume), 
including  liquid,  dry,  and  cubic  measures. 

6.  State  some  units  suggested  by  these  numbers  : 

If         0.125         325  ft.         263  bu.         5000         300 

7.  In  the  fraction  |J,  what  is  the  fractional  unit  ?  What 
term  of  the  fraction  tells  you  this?  What  term  tells  how 
many  such  units  are  taken?  ^oavw^^o^^^^^ 

WRITTEN  EXERCISE 

1.  Express  233  units,  each  unit  being  ^^^  ;  1  ft.;  0.001. 

2.  Express  in  terms  of  the  next  smaller  unit  in  the  table : 
37.5  ft.,  48  gal.,  23  mi.,  48  yd.,  75  lb.,  6  T.,  81  sq.  ft. 

3.  Express  in  terms  of  the  next  larger  unit  in  the  table : 
37  in.,  42  ft.,  36  oz.,  960  rd.,  4000  lb.,  100  qt.,  1728  in. 

4.  Express  in  terms  of  the  unit  1  in.  the  following  :  9  rd.., 
7  yd.,  6  mi.,  4  ft.,  3  yd.,  7  ft.,  3J  ft.;  7J  yd.,  ^  rd.,  2]^m\. 


WRITING  NUMBERS 


ORAL   EXERCISE 


■^  '   1.    In  the  common  fraction  |,  name  the  terms  and  tell 
what  each  expresses  about  the  fraction. 

2.  The  fraction  \  may  be  thought  of  as  meaning  3  of 
what  parts  of  a  unit?  Or  it  may  be  thought  of  as  \ 
of  how  many  units? 

3.  If  a  yard  is  called  one^  a  foot  will  be  called  what 
fraction?  An  inch  will  be  called  what  fraction?  A  rod 
will  be  called  what  mixed  number? 

4.  How  is  a  fraction  reduced  to  lower  terms  ?  When  is 
it  said  to  be  in  its  lowest  terms  ?  Why  do  you  ever  need 
to  reduce  fractions  to  lowest  terms  ? 

5.  How  do  you  proceed  to  add  one  fraction  to  another  ? 
to  subtract  one  fraction  from  another  ?    Why  is  this  ? 

6.  How  do  you  know  that  J  of  J  =  J  ?  Illustrate  at  the 
board  by  taking  ^  of  J  of  a  foot.  Show  also  that  \  oi  \ 
has  the  same  value  as  \  of  \. 

WRITTEN   EXERCISE 

1.  Draw  a  rectangle  1  in.  long.  Find  J  of  :|  of  it;  also 
J  of  ^  of  it.    Show  that  \  of  i  =  \oi\, . 

2.  In  the  same  way  show  by  a  line  that  2  times  \  in.  = 
§  in.,  and  that  J  of  2  in.  =  f  in. 

3.  Find  the  value  of  ^  of  f  in.,  representing  the  work 
by  lines.     Also  find  the  value  of  f  of  ^  in. 

4.  In  the  same  way  show  that  f  of  §  in.  =  y\  in. ;  also 
that  f  of  f  in.  =  -^  in. ;  also  that  f  of  f  =  f  of  f . 

\  5.  Mark  an  inch  line  into  halves,  and  also  into  thirds. 
Show  from  it  that  the  ratio  of  ^  to  ^  is  3  :  2^  or  that 
J.  -H  J  =  |.     Show  also  that  \^\=^\, 


I 


SCALES  7 

ORAL   EXERCISE 

1.  Eead  :  2^,  2  ft.  3  in.    Explain  the  difference  in  scales. 

2.  Eead :  5.8,  5  lb.  8  oz.,  5  hr.  8  min.     State  the  scales. 

3.  Kecite  the  tables  of  length,  square  measure,  cubic 
measure,  dry  and  liquid  measure,  weight,  United  States 
money,  and  time ;  also  the  table  of  dozens  and  gross. 

4.  Express  as  inches  :  2  ft.  3  in.,  5  ft.  8  in.,  100  ft.  9  in., 
1  yd.,  1  yd.  2  in.,  1  yd.  1  ft.,  1  yd.  10  in. 

5.  Express  as  feet :  3  yd.,  3  yd.  2  ft.,  7  yd.,  7  yd.  1  ft., 
10  yd.,  60  in.,  2  rd.,  4  rd.,  2  rd.  3  ft.,  2  rd.  2  yd. 

6.  Express  as  pounds  or  fractions  of  a  pound :  32  oz., 
8  oz.,  4  oz.,  1  T.,  2  T.,  3^  T.,  4  cwt.,  1  T.  2  cwt. 

7.  Express  as  quarts,  liquid  or  dry  as  the  case  may  be: 
20i  gal,  2  gal.,  2  bu.,  3  pk.,  2  pt.,  5  gal.  2  qt.,  2  pk.  1  qt. 

WRITTEN   EXERCISE 

1.  Write  3456  as  dozens ;  as  gross  ;  as  great  gross. 

2.  Write  as  inches  :  17  ft.,  21  ft.  6  in.,  3  yd.,  4  rd. 

3.  Write  as  feet :  36  in.,  144  in.,  1728  in.,  54  yd.,  J  rd. 

4.  Write  as  pounds :  2^  T.,  3.25  T.,  144  oz.,  3  T. 
1520  lb.,  4  cwt.  27  lb.,  1584  oz. 

5.  Write  as  quarts  :  53  gal.,  26  bu.,  17  gal.  3  qt.,  98  pt., 
31  bu.  2  pk.,  31^  gal.,  75|  gal.,  17^  bu. 

^—  6.   Express  as  units  :  6  gross  3  doz.,  7^  gross,  15j  doz., 
6  great  gross,  15|  doz.,  J  doz.,  27^  gross. 

7.  Explain  what  is  meant  by  a  uniform  scale  ,•  a  varying 
scale.     Give  an  illustration  of  each. 

8.  Tell  why  a  varying  scale  is  not,  in  general,  so  good  as 
a  uniform  scale.     Illustrate  by  examples. 


ADDITION 


ADDITION  REVIEWED 


8.  The  principle  of  addition.  The  principle  of  addition  is 
the  same  whether  we  add  integers,  fractions,  denominate 
numbers,  or  expressions  containing  letters. 


(1) 

(2) 

(3) 

6  8 

6.8 

6A 

9  7 

9.7 

Vr 

(15)(15)  = 

(15)-(15)  = 

15H  = 

165,  because  15 

16.5,  because 

16-|-\,  because 

units  = 

1  ten  + 

16  tenths  =  1 

H  =  1  A- 

5  units. 

+  6  tenths. 

In  each  case  the  number  of  units  is  the  same.  In  each  the 
addition  7  +  8  requires  us  to  add  1  to  the  next  higher  order. 

In  oral  addition,  as  of  68  and  97,  it  is  usually  better  to  begin  at 
the  left.  In  this  case  say  :  "  97, 157,  165  ";  that  is,  97  +  60  =  157, 
157  +  8  =  165. 


ORAL    EXERCISE 

Ad 

Id^  stating  only  the 

answers: 

1. 

23 

2.    61 

3.  37 

4. 

29 

5. 

34 

49 

28 

48 

63 

48 

6. 

34 

7.  26 

8.  82 

9. 

68 

10. 

47 

85 

96 

75 

68 

53 

11. 

121 

12.  132 

13.  126 

14. 

235 

15. 

128 

69 

48 

57 

75 

89 

16.  Add  2  in.,  3  in.,  3  in.,  7  in.,  11  in.  Express  the  result 
also  as  feet  and  a  fraction ;  as  feet  and  inches. 

17.  What  do  we  mean  by  addition  ?  by  addends  ?  by  the 
sum?  How  do  we  check  (or  prove)  our  additions?  Give 
examples. 


ADDITION 


WRITTEN   EXERCISE 


Add,  checking  (proving)  the  work  hy  adding  in  reverse 
order.    Time  yourself. 


1.  472 

2.  47  ft.  2  in. 

3. 

4  mi 

•  7  yd. 

,2  ft. 

4. 

47  bu.  2  pk. 

691 

69      1 

6 

9 

1 

69        1 

580 

68 

6 

8 

68 

432 

43      2 

4 

3 

2 

43       2 

841 

84      1 

8 

4 

1 

84       1 

670 

67 
Reduce  §,  |,  ^  to 

U 

5 

7 

Al 

67 

5.    ] 

felfths  and  add. 

so  reduce  to 

twenty- 

fourths  and  add. 

6.  Keduce  i,  |,  ^  to  eighths  and  add.  Also  reduce  to 
decimal  fractions  and  add,  checking  by.  reducing  the  result 
to  an  integer  plus  a  common  fraction. 

7.  Add  J,  f ,  I,  by  reducing  to  sixths ;  to  twelfths ;  to 
eighteenths.    Show  that  the  results  are  equal. 

8.  Add  J,  I,  |,  f,  -/^.  (Which  is  the  better  plan  in  this 
case,  to  reduce  to  the  denominator  120,  or  to  decimal 
fractions  ?) 

9.  Add  f ,  f ,  J,  f,  ^-Q.  (To  what  common  denominator 
may  these  fractions  be  reduced?  Is  it  better  to  reduce  to 
decimal  fractions  ?    Why  ?) 


10.  Add  the 

following : 

5x  +  ly 

501 

5  ft.  1  in. 

61b.  loz. 

6a;  +  5y 

605 

6 

5 

6      5 

4:X  +  Zy 

403 

4 

3 

4      3 

Ix  +  Qy 

706 

7 

6 

7       6 

9a;4-8y 

908 

9 

8 

9      8 

Notice  that  the  first  of  these  results  reduces  to  the  second  if 
X  =  100  and  y  =  1 ;  to  the  third  if  a;  =  1  ft.,  y  =  ^^  ft.,  or  1  in.; 
to  the  fourth  if  a:  =  1  lb.,  y  =  ^^Vo.,  or  \  oz. 


10  ADDITION 

Add^  checking  the  work  hy  adding  in  reverse  order. 
Time  yourself. 

11.    $31.50  12.  $62.35  13.  $20.00  14.  $35.75 

26.75  49.82  35.40  87.66 

15.42  81.46  20.76  92.33 

51.13  73.98  83.92  83.47 

73.06  20.05  99.81  62.54 

52.70  30.00  78.56  81.35 


15.    $312.75  16.  $402.75  17.  $209.81  18.  $175.54 

63.40  75.75  801.19  2%^AQ> 

281.00  163.87  634.77  87.92 

127.05  91.83  75.23  93.41 

31.63  182.48  62.97  62.78 

428.70  328.62  47.03  88.39 


19.     $486.83  20.  $128.92  21.  $634.81  22.  $189.98 

642.75  871.08  528.92  235.42 

208.05  346.52  365.19  628.75 

100.00  853.50  471.08  832.63 

378.92  671.18  275.50  798.49 

604.83  832.00  325.50  629.36 


23.  $1276.35    24.  $3246.81     25.  $8234.61      26.  $2983.41 

397.63  2981.26  8327.92  3872.62 

428.42  583.42  2842.68  2987.48 

608.70  629.87  178.53  293.29 

2304.69-  3473.92  296.48  981.50 

572.96  Q^2M  378.75  6287.49 

3270.05  2987.62  2876.92  832.08 


ADDITION 


11 


27.  The  following  are  some  recent  statistics  of  the  great 
industries  of  the  United  States. 


Industry 

Ill 

£■1 

m 

r3 

5| 

Wool  Manuf.     . 

2,636 

$415,075,713 

264,021 

$92,499,262 

$250,805,214 

$427,905,020 

Cotton  Manuf.  . 

1,051 

467,240,157 

302,861 

86,689,752 

176,551,527 

339,198,619 

Iron  and  Steel   . 

661 

573,119,275 

222,264 

120,723,092 

522,071,772 

803,344,591 

Meat  Industry  . 

921 

189,198,264 

68,534 

33,457,013 

683,5&3,577 

786,603,670 

Lumber     .     .    . 

33,035 

611,611,524 

283,260 

104,640,591 

317,923,548 

566,832,984 

Flour     .... 

25,258 

218,714,104 

37,073 

17,703,418 

475,826,345 

560,719,063 

Boots  and  Shoes 

1,600 

101,795,233 

142,922 

59,175,883 

169,604,054 

261,028,580 

Publishing     .    . 

15,305 

192,443,708 

94,604 

50,214,051 

50,214,904 

222,983,569 

Find  the  sums  of  the  various  columns. 

Pupils  should  be  timed  in  all  such  work,  and  accuracy  should  be 
insisted  upon  by  requiring  checks. 

28.  The  following  are  some  of  the  wealthiest  countries 
in  the  world  according  to  recent  statistics,  with  the  approxi- 
mate money  which  each  has. 


Country 

li 

1^ 

III 
1^^  . 

3^1 

Mi 

United  States     . 

85,000,000 

$1,174,600,000 

$660,000,000 

$437,800,000 

France    .... 

40,000,000 

903,500,000 

419,800,000 

134,500,000 

Great  Britain 

42,000,000 

528,000,000 

116,800,000 

116,200,000 

Germany    .    ,     . 

57,000,000 

762,800,000 

207,500,000 

153,400,000 

Russia    .... 

131,000,000 

714,600,000 

103,200,000 

Austria-Hungary 

47,100,000 

257,000,000 

80,000,000 

39,900,000 

Australasia     .    . 

5,500,000 

128,600,000 

6,100,000 

Add  the  columns.  Fill  the  last  column  by  adding  the 
three  preceding  columns  crossways  to  the  right.  How 
will  you  check  the  work? 


12  SUBTRACTION 

SUBTRACTION  REVIEWED 

9.  The  principle  of  subtraction.  The  principle  of  subtrac- 
tion is  the  same  whether  we  subtract  integers,  fractions, 
denominate  numbers,  or  expressions  containing  letters.  The 
general  principle  is  seen  in  the  following : 

(1)  (2)                    (3)  (4) 

61  6.1  6J  6  ft.    1  in. 

23  2^  2|  2         3 

38  3.8  3|  =  3i  3  ft.  10  in. 

In  each  case  the  number  of  units  is  the  same.  In  each 
case  the  subtraction  1  —  3  requires  us  to  increase  the  1  by 
a  unit  of  the  next  higher  order  before  subtracting. 

In  oral  subtraction,  as  of  23  from  61,  it  is  usually  better  to 
begin  at  the  left.  In  this  case  say :  "  61,  41,  38 " ;  that  is, 
61  -  20  =  41,  41  -  3  =  38. 

ORAL   EXERCISE 

Subtract^  stating  only  the  answers : 


82 

2. 

63 

3. 

72 

4. 

81 

5. 

73 

2T 

19 

35 

24 

49 

67 
38 

7. 

42 
18 

8. 

95 
58 

9. 

90 
32 

10. 

86 
39 

102 

12. 

105 

13. 

204 

14. 

125 

15. 

143 

43 

36 

95 

67 

85 

11. 


16.  What  is  meant  by  saying  that  ^^only  units  of  the 
same  kind  can  be  added  "  ?     Can  you  not  add  $2  and  3  ct.  ? 

17.  What  is  meant  by  saying  that  "only  units  of  the 
same  kind  can  be  subtracted "  ?  Can  you  not  subtract 
3  ct.  from  $2  ? 


SUBTRACTIO]vr  13 

WRITTEN   EXERCISE 

Subtract^  checking  each  result  hy  adding  the  subtrahend 
and  remainder.     Time  yourself. 


1. 

$287.50 

2.  $351.75 

3.  $429.35 

4.  $526.41 

132.95 

268.19 

228.92 

229.37 

5. 

$391.11 

6.  $629.48 

7.  $802.05 

8.  $329.90 

287.52 

297.63 

120.70 

100.95 

9. 

$1235.00 

10.  $2634.05 

11.  $1963.00 

12.  $5283.75 

926.75 

827.50 

298.50 

1296.55 

3. 

$285.42 

14.  285  mi. 

42  ft.     15. 

285  T.  42  lb. 

196.55 

196 

65 

196  bb 

Notice  the  similarity  of  the  figures  used  in  Exs.  13-15. 

16.  $5432      17.  54  mi.  32  ft.      18.  54  T.  32  lb. 
2354         23    54  23   54 


Notice  the  similarity  of  the  figures  used  in  Exs.  16-18. 

19.  $1,725,342,628  -  $632,487,129. 

20.  $27,142,628,341  -  $16,923,437,286. 

21.  $2,421,002,625.25  -  $1,278,101,123.50. 

22.  372        23.  3.72         24.  37  ft.  2  in.         25.  37  lb.  2  oz. 
153  1^  15       3  15        3 

26.  2  yd.  1  ft.  27.  2  T.  1  lb.  28.  2  yr.  1  mo. 

12  12  12 


29.  1915  yr.  2  mo.    3  da.  30.  1920  yr.  0  mo.    6  da. 

1906        8         15  1909        2         17 

31.  Write  out  in  your  own  way  a  statement  of  your 
method  of  adding  numbers. 

32.  Write  out  in  the  same  way  a  statement  of  your 
method  of  subtracting  numbers. 


14 


SUBTRACTION 


33.  2738f  - 

-  1299f 

35.  6592J- 

-  4289f . 

37.  72911- 

-  2986f . 

*  34.  87211 -1796|. 
36.  2872f-1628j. 
38.    9289|  -  2691^5^. 

39.  40  ft.  4i  in.  -  27  ft.  9i  in. 

40.  172  lb.  51^  oz.  -  69  lb.  lOf  oz. 

41.  426  gal.  If  qt.  -  197  gal.  3J  qt. 

42.  1345.25  +  175f  +  375  -  (f  +  J  +  |). 

43.  234  sq.  ft.  9i  sq.  in.  -  175  sq.  ft.  98f  sq.  in. 

44.  148  cu.  ft.  521 J  cu.  in.  -  69  cu.  ft.  827J  cii.  in. 

45.  321  da.  6  hr.  2  min.  15  sec.  -  125  da.  7  hr.  21.75  sec. 
^  46.    273  da.  5  hr.  3  min.  17  sec.  -  169  da.  23  hr.  43.25  sec. 

47.  The  savings  bank  depos- 
its in  this  country  for  the  years 
1900-1904  are  indicated  in  this 
table.  Find  the  increase  for 
each  year.  Also  find  the  in- 
crease of  1904  over  1900. 

48.  The  five  states  having  the  largest  population  are 
here  given,  with  the  population 

according  to  a  recent  census,  ^^w  York  .  .  7,268,894 
The  population  of  New  York  Pennsylvania  6,302,115 
was  how  much  more  than  that  ^^^^^^^^  •  •  •  4,821,550 
of  each  other  state?  ^^^^-     '     •     -4,157,545 

Missouri     .     .   3,106,665 
,^       49.   By  the  table  of  Ex.  48, 

the  population  of  Pennsylvania  was  how  much  more  than 
that  of  Illinois  ?    of  Ohio  ?    of  Missouri  ? 

50.   By  the  same  table,  the  population  of  Illinois  was 
how  much  more  than  that  of  Ohio  ?    of  Missouri  ? 


1900  . 

.  2,449,647,885 

1901  . 

.  2,697,094,580 

1902  . 

.  2,750,177,290 

1903  . 

.  2,936)204,845 

1904  . 

.  3,060,178,611 

^ 


MULTIPLICATION  15 

MULTIPLICATION  REVIEWED 

10.  The  principle  of  multiplication.    The  principle  of  multi- 
plication is  the  same  for  all  numbers. 
$7.50  7  ft.    5  in. 

9  9 

4.50  =  9  times  $0.50  45  in.  =  9  times         5  in. 

63       =''      "     $7  63  ft.  =''      "     7  ft. 


$67.50-"      "     $7.50  66  ft.    9  in.  = "      "     7  ft.  5  in. 

In  each  case  the  number  of  units  is  the  same.  The  results 
differ  because  the  first  number  is  on  the  scale  of  10,  the  second 
on  the  scale  of  12. 

The  principle  is  the  same : 

Multiply  the  denominatio7is  or  orders  separately.  Then 
add  the  partial  products,  simplifying  when  possible. 

In  oral  multiplication,  as  of  $7.50  by  9,  it  is  usually  better  to 
begin  at  the  left.     In  this  case  we  say :   "  $63,  $4.50,  $67.50." 

ORAL   EXERCISE 

Multiply^  stating  only  the  answers : 
1.    2^  2.    37  3.    33  4.    43  5.    53 

_2  _3  _4  _5  _6 

6.    25  7.    32  8.    54  9.    Q>Q  10.    70 

_7  _8  _9  11  12 

11.    $2.50     12.    $7.50     13.    $8.20     14.    $3.30    15.    $5.50 
5  6  7  8  9 

16.  What  is  meant  by  saying  that  the  multiplier  must 
always  be  an  abstract  number?     Illustrate. 

17.  What  is  meant  by  saying  that  the  product  must 
always  be  of  the  same  denomination  as  the  multiplicand? 


16  MULTIPLICATION 


WRITTEN   EXERCISE 


Multiply  as  indicated^  noticing  the  similarity  in  the 
figures  of  the  multiplicands: 

1.  By  7  :  175,  17  ft.  5  in.,  1  mi.  75  ft. 

2.  By  37 :  427,  42  lb.  7  oz.,  4  mi.  27  rd. 

3.  By  13  :  936,  $9.36,  93  ft.  6  in.,  9036. 

4.  By  26  :  428,  4  sq.  ft.  28  sq.  in.,  4028. 

5.  By  1325:  $63.25,  63  mi.  25  rd.,  63,025. 

6.  By  59  :  $19.20,  19  gal.  2  qt.,  19  yd.  2  ft. 

7.  By  2007:  $1271.50,  127  da.  1  hr.  50  miu. 

8.  By  625  :  1728,  17  sq.  ft.  28  sq.  in.,  17,028. 

Multiply^  writing  the  number  of  minutes  required  for 
Uxs,  9-33: 


^ 

9.  2765 
127 

10.  3402 
348 

11. 

4246 
293 

12.  1563 
892 

13.  4762 

987 

14.  2983 
896 

15. 

5786 
469 

.^16.  5999 
987 

^17. 

$175.27 
325 

18. 

$287.62 
625 

19.  $482.92 
328 

20.  $576.75 
476 

21. 

$247.60 
908 

22. 

$409.75 
607 

23.  $507.63 
806 

24.  $707.07 
999 

^25. 

27  ft.  8  in. 
17 

z. 

26.  29  ft.  9  in. 
32 

27 
30. 
33. 

.  m  ft.  4  in. 
43 

^28. 

82  ft.  7  in. 
68 

29.  12  It 

).  8  oz. 

2 

16  lb.  9  oz. 
23 

^  31. 

17  lb.  15  o: 

27 

32.  231b 

».  4  oz. 
24 

24  ft.  9  in. 
48 

MULTIPLYING  BY  FRACTIONS  17 

11.  Multipl3ring  by  fractions.  In  multiplying  by  fractions 
we  may  use  the  following  forms  to  show  the  similarity, 
although  we  have  shorter  ones  for  actual  work. 

69  69  6.9  f 

A  A  ^  1. 

23  =  Jof69       6.9  =  .lof69       .69  =  .lof6.9     j%  =  i  of  i 

_2  _2  2  2_ 

46  =  |of69     13.8  =  .2of69     1.38  =  .2of6.9     A^fofJ 

In  multiplying  69  by  |  we  simply  think  that  J  of  69  is  23,  and 
we  multiply  (mentally)  23  by  2. 

In  multiplying  6.9  by  .2  we  simply  think  that  tenths  multiplied 
by  tenths  is  hundredths,  and  we  multiply  69  by  2  and  express  the 
result  as  hundredths. 


To  multiply  3 J  by  2^  we  may  say: 

2^  =  ^, 

2      2 

'r 

10      6      Xj3 

26        1 
3-  =  ^3- 

ORAL   EXERCISE 

1. 

foff 

2. 

f  off 

3. 

f  off. 

4. 

|of|. 

5. 

ioff 

6. 

ioff 

7. 

Joff. 

8. 

i  Of  |. 

9. 

i  of  j%. 

.10. 

§  of  f . 

11. 

i  Of  if 

12. 

1  of  IJ. 

13. 

i  of  J  of  i. 

/14. 

i  of  f  of  3. 

15. 

f  of  1  of  f. 

16. 

f  of  1  of  8. 

17. 

§  of  1  of  10. 

18. 

4  of  f  of  7. 

19. 

«  of  i  of  If. 

20. 

2  of  i  of  14. 

^21. 

1  off  of  50. 

,22. 

i  of  2i. 

23. 

i  of  H. 

24. 

iof3^. 

25. 

f  of  44. 

26. 

§  of  33. 

27. 

§  of  li. 

28. 

f  of  49. 

29. 

1  of  77. 

^30. 

|of  25. 

31.  How  much  will  |  yd.  of  silk  cost  at  64/  a  yard  ? 

32.  How  much  will  J  yd.  of  velvet  cost  at  $1.60  a  yard? 


18  MULTIPLICATION 


WRITTEN   EXERCISE 

.5  X  324. 

2.   3|  X  65. 

3.    92  X  72. 

of  73i. 

5.    1  of  16|. 

6.    *  of  19^. 

'h  X  3f. 

8.    4f  X  6|. 

9.    5i  X  6^. 

10.  State  a  brief  rule  for  multiplying  by  a  decimal  frac- 
tion.    Illustrate  by  0.3  of  0.22. 

11.  State  a  brief  rule  for  multiplying  one  common  frac- 
tion by  another.     Illustrate  by  f  of  f. 

Multiply  as  indicated^  timing  yourself: 


12. 

23.4 

13. 

17.6 

14. 

35.7 

15. 

82.7 

4.5 

^.4 

6.9 

9.8 

16. 

99.8 

17. 

2.75 

18. 

7.48 

19. 

8.09 

7,9 

.35 

1.25 

8.09 

^   20. 

.632 

21. 

.473 

22. 

6.42 

23. 

89.2 

8.25 

2.48 

3.27 

62.8 

24. 

34.9 

26. 

1.472 

26. 

6.043 

27. 

2.481 

30.5 

3.25 

1.37 

6.25 

28. 

0.735 

29. 

1.326 

30. 

2.307 

31. 

298.7 

6.25 

4.32 

53.6 

.634 

^32. 

812.8 

33. 

296.4 

34. 

82.32 

35. 

487.6 

.437 

.0124 

.063 

2.083 

36. 

$14.92 

37. 

$15.75 

38. 

$14.87 

39. 

$65.04 

2.35 

3.42 

2.91 

9.09 

,40. 

1484 

41. 

2636 

42. 

3792 

43. 

178.32 

/ 

3.2i 

4.1i 

6.23J 

1.24f 

MULTIPLYING  BY  FRACTIONS  19 


44. 

49.74 

45. 

82.49 

46. 

693.4 

y 

.0426 

.0487 

83.7 

47. 

Hofif. 

48. 

II  of  T%. 

49. 

\\  of  f  J. 

50. 

Mof||. 

51. 

If  of  If. 

52. 

H  of  if. 

53. 

$327.76 

54. 

$139.83 

55. 

$164.24 

13i 
$325.84 

57. 

37f 
$841.40 

58, 

34| 

56. 

$935.44 

39i 

63| 

87f 

59. 

21  ft.  8  in. 

60. 

38  lb.  2  oz. 

61. 

62  yd.  27  in. 

15i 

23| 

25f 

62.  127fxl354-.     63.   229|x213|.     64.    723f  X  734.8. 

65.  209|x  235.5.     66.    327-1 X  3331.     67.    187t\x175J. 

68.  At  $1.56  a  yard,  what  will  14|  yd.  of  silk  cost? 

69.  At  $1.28  a  yard,  what  will  37|  yd.  of  carpet  cost? 
^  70.  At  $5.60  a  ton,  what  will  17  T.  2501b.  of  coal  cost? 

71.  What  is  the  cost  of  37i  rd.  of  fence  at  $1.12i^  a  rod? 

72.  When  hay  is  selling  at  $9|  a  ton,  what  will  23^  T. 
cost? 

/  73.    What  is  the  number  resulting  from  taking  32  ft.  9  in. 
as  an  addend  37  times  ? 

74.  At  78 1  lb.  to  the  yard,  what  is  the  weight  of  a  mile 
of  double  rails  for  a  track? 

75.  A  hexagon  of  equal  sides  is  measured,  and  each  side 
is  found  to  be  19^2  i^^-     What  is  the  perimeter  ? 

76.  What  is  the  number  resulting  from  taking  17f  as 
an  addend  23  times,  and  then  adding  \  of  17f  to  the  sum  ? 


20  DIVISION 

DIVISION  REVIEWED 

12.  Nature  of  division.  We  have  seen  that  division  is  the 
inverse  of  multiplication.  _  That  is, 

because  2.5  times  $40  =  $100, 

therefore  $100  --  $40  =  2.5, 

and  $100  -  2.5  =  $40. 

13.  Two  cases.   There  are,  therefore,  two  cases  of  division  : 

1.  If  the  dividend  and  divisor  are  like  numbers,  the 
quotient  is  abstract. 

2.  If  the  dividend  is  concrete  and  the  divisor  abstract,  the 
quotient  is  like  the  dividend. 

14.  Similar  classes  in  the  first  case.  The  similarity  for 
various  classes  of  numbers  appears  from  the  following : 

572  ft.  -^  24  in.  may  be  reduced  to  572  ft.  -h  2  f t.  =  286, 
or  it  may  be  reduced  to  6864  in.  -^  24  in.  =  286 ; 

55.2  -r-  0.24  may  be  reduced  to  55.20  h-  0.24,  and  treated 
as  if  it  were  5520  --  24  =  230  ; 

§  -T-  f  may  be  reduced  to  |g  -j-  |§,  and  treated  as  if  ib 
were  10  -h  12  =  |.     (See  §  20  for  the  practical  work.) 

That  is,  in  this  case,  dividend  and  divisor  are  reduced  to 
like  numbers,  or  denominations,  before  dividing. 

15.  Similar  classes  in  the  second  case.  In  the  second  of 
these  cases  the  similarity  for  various  classes  of  numbers 
appears  from  the  following  examples : 

$10  -f-  .8  =  $100  --  8,  by  multiplying  each  by  10 ; 

$10  --  f  =    $50  --  4,   "  ''  "      "  5, 

although  we  have  a  simpler  method  for  dividing  common 
fractions,  as  explained  in  §  20,  where  it  is  shown  that 
10  -  J  =:=  10  X  J  =  121. 


X 


DIVISION  21 
ORAL   EXERCISE 

Divide  as  indicated  in  Exs.  ISO : 

1.    355-5.                2.    424-4.  3.  126-^3. 

4.    275  -  5.                5.    536  -  4.  6.  315  -f-  3. 

7.    636-6.                8.    637-7.  9.  728-8. 

10.    189-9.              11.    217-7.  12.  640 -^  8. 

13.    819-9.              14.    504-7.  15.  ^m-^%. 

16.    121-11.            17.    144-12.  18.  156-12. 

19.    143-13.            20.    154-14.  21.  315-^15. 

22.   320-16.            23.    510-17.  24.  360-^18. 

25.    620-20.            26.   420-21.  27.  660-22. 

28.    253 -V- 23.            29.    144-24.  30.  625-25. 

Divide  as  indicated  inExs,  31-Jf5^  stating  the  remainders : 
That  is,  186  -^-  17  =  10,  and  16  remainder. 

31.    $145  H- 12.         32.    $136^13.  33.  $150^14. 

34.    $157  H- 15.         35.    $330-16.  36.  $181^17. 

37.    $193  ^$18.       38.    $200 -$19.  39.  $219  -  $20. 

^40.    $430 -$21.       41.    $444 -$22.  42.  $691  h- $23. 

43.    723  ft. -24.       44.    630  yd. -25.  45.  631  in.  -  30. 

Divide  as  indicated  in  Exs,  4^-63^  including  fractions  in 
the  quotients  : 

That  is,  186  -^  17  =  10}f. 

46.    1526-5.        ^47.    2751-5.  48.  6017-^5. 

49.   2419-2.            50.   3221-2.  51.  1683-^2. 

52.    3631-3.            53.    1234-3.  54.  6094-3. 

^55.    4805-4.            56.    8005-4.  57.  6013-^6. 

58.    7146-7.            59.    8009-8.  60.  8183^9. 

61.    6477  -^  10.     ^  62.    5239  ^  10.  .63.  1211  ^  11. 


22  DIVISION 

16.  General  principle  of  division.  We  have  learned  how 
to  divide  by  long  division  and  by  short  division.  The  gen- 
eral principle  is,  however,  the  same  for  both.  Consider  the 
case  of  625  -T-  2^, 

25  25)625 

25)625  25 

500  =  20  times  25  is  the  same  as 

125  25)500  +  125 

125=    5      "     25  20  4-5  =  25 

In  each  case  we  see  that  600  -4-  25  =  no  hundreds ;  620  -r-  25 
=  2  tens,  for  2  tens  x  25  =  500,  and  there  is  125  left  to  be 
divided.     Also,  125  -^  25  =  5.     Therefore  the  result  is  25. 

17.  Division  by  a  decimal.    In  dividing  by  a  decimal  frac- 
y  ^Jionn-ulmays  WMlti^ph^  both  dividend_jbnd  divisor  hy  such  a_ 

^number  as  shall  make  the  divisor  a  ivhole  number. 

Thus,  in  the  case  of  62.5  -4-  0.25,  multiply  both  by  100  and 
divide  6250  by  25. 

WRITTEN   EXERCISE 

1.  Divide  987  by  35  and  write  out  the  explanation. 

2.  Divide  575  by  25  in  the  three  ways  shown  above. 

3.  Divide  506  by  22  in  the  three  ways  shown  above. 

4.  At  261  ct.  a  yard,  how  many  yards  of  cloth  can  be 
bought  for  $36.57?  If  138  yd.  cost  $36.57,  what  will 
1  yd.  cost  ? 

6.  Derby  hats  cost  from  $24  to  $42  a  dozen.  Make  up 
two  problems,  similar  to  those  in  Ex.  4,  state  them,  and 
solve. 

6.  Name  and  define  the  four  terms  used  in  division. 

7.  Write  out  a  rule  for  dividing  one  number  by  another. 


DIVISION  23 

Divide  as  indicated^  seeing  how  many  problems  you  can 
solve  in  jive  minutes  ;  in  ten  minutes  : 

8.  1554-37.  9.    1924-52.  10.    2793-57. 

11.  3844  -  62.  12.    5593  -  49.  13.    2701  -  73. 

14.  5402-37.  15.    3402-81.  16.    1225-18. 

17.  1089-33.  18.    6822-36.  19.    8888-808. 

20.  5203-121.        21.    20,273-97.       22.    17,841-57. 

23.  2541-121.        24.    20,698-98.       25.    22,248-72. 

26.  10,449  -  81.       27.    13,024  -  407.     28.    14,838  ^  209. 

29.  30,092  -  121.     30.    27,968  -  304.     31.    17,094  -  777. 

32.  80,091  -  809.     33.    19,908  -  237.     34.    14,985  -  m^. 

35.  4291)55,783.      36.    2075)47,725.      37.    6772)277,652. 

38.  3227)203,301.     39.    7407)674,037.     40.    2469)224,679. 

41.  $569.25-124.75.  42.    $570.24  -  $17.82. 

43.  $1309.00  -  $29.75.  44.    $2521.48  ^  $48.49. 

45.  If  35  floor  tiles  together  weigh  113.75  lb.,  what  is 
the  average  weight  of  each  ? 

46.  If  $1548  is. divided  equally  among  a  dozen  persons, 
how  much  is  the  share  of  each  ? 

47.  If  $2193.75  is  divided  equally  among  15  persons, 
how  much  is  the  share  of  each  ? 

^---48.    If  a  piece  of  land  containing  12.75  acres  is  cut  into 
17  equal  building  lots,  what  is  the  area  of  each  ? 

49.  If  the   dividend  is  420,  the   quotient  32,  and  the 
remainder  4,  what  is  the  divisor? 

50.  If  the  dividend  is  73  times  the  remainder,  and  the       O 
quotient  is  24,  and  the  divisor  is  12,  what  is  the  remainder  ? 


2  ft. 

3 

in. 

15)33  ft. 
30  " 

9 

in. 

3ft.= 

=  36 
45 
45 

in. 
in. 

24  DIVISION 

18.  Division  of  denominate  numbers  by  abstract  numbers. 
Divide  33  ft.  9  in.  by  15. 

We  divide  33  ft.  by  15  and  have  2  ft., 
with  a  remainder  of  3  ft.,  which,  reduced 
to  inches  (36  in.)  and  added  to  9  in., 
equals  45  in.,  which  is  still  to  be  divided. 
Again,  45  in.  h-  15  =  3  in. 

19.  Division  of   denominate  numbers  by  denominate  num- 
bers.    Divide  23  ft.  4  in.  by  3  ft.  4  in.     Here  either 

1.  23  ft.  4  in.  H-  3  ft.  4  in.  =  23i  ft.  ^  3J  ft.  =  -'^  ft.  ^  -Lo  ft.  =  7 ;  or 

2.  23  ft.  4  in.  H-  3  ft.  4  in.  =  280  in.  -^  40  in.  =  7. 

In  the  first  case  we  reduce  to  feet ;  in  the  second,  to  inches. 

WRITTEN   EXERCISE 

1.  2043  gal.  3  qt.  -  25.  2.  430  yd.  10  in.  -  11. 

3.  213  ft.  9  in.  --  23  ft.  9  in.     4.  652  ft.  -f-  81  ft.  6  in. 

5.  518  yd. --42  yd.  3  ft.  6  in.    6.  1587  lb.  -  132  lb.  4  oz. 

/  7.  355  hr.  33  min.  45  sec.  -v- 15. 

8.  4868  cu.  ft.  1200  cu.  in.  --  23. 

9.  22  hr.  40  sec.  --  5  hr.  30  min.  10  sec. 

/  10.   How  much  is  an  eighth  of  116  lb.  8  oz.  ? 

11.    4557  sq.  ft.  54  sq.  in.  -^  147  sq.  ft.  90  sq.  in. 
/  12.    How  much  is  half  of  2  hr.  53  min.  18  sec? 
13.    How  much  is  a  quarter  of  11  yd.  2  ft.  8  in.  ? 

N14.  If  a  cubic  foot  of  gold  weighs  1187  lb.  8  oz.,  and  if 
gold  is  19  times  as  heavy  as  water,  what  does  a  cubic  foot 
of  water  weigh  ? 

^  15.  If  it  takes  a  man  8  hr.  31  min.  24  sec.  to  walk  a 
certain  distance,  how  long  will  it  take  an  automobile  to 
travel  the  same  distance,  if  it  goes  12  times  as  fast  ? 


DIVIDING  FRACTIONS 


26 


ORAL  EXERCISE 

1.  Tell  why  f  -^  2  =  ^ ;  also  why  J  -^-  2  =  i . 

2.  Tellwhyl^J  =  3;  also  why  2--^  =6,  and  5-^^  =  15. 

3.  Because  5-^^  =  15,  tell  why  5^%=^Qi  15,  or  -y . 

4.  Because  5  -;-  |  =  y ,  tell  why  f  ^  §  =  |  of  -i/,  or  ||. 

5.  Because  f  -^  f  =  yi?  ^^^  because  J  of  f  =  |  j,  what 
operation  may  be  performed  in  place  of  dividing  one  frac- 
tion by  another  ? 

20.  Dividing  fractions.    In  dividing  |  by  §,  we  may 

1.  H educe  to  a  common  denominator  and  divide  the  new 
numerators.  ^^  -f-  ^4  =  ||^  j^st  as  $15  -t-  $14  =  ||,  or 
15  ft.  -f- 14  ft.  =  i|.    Or  we  may 

2.  Invert  the  divisor  and  multiply.  That  is,  f  -^  f  =  7 
X  I  =  ||.  We  use  this  operation  rather  than  the  other, 
because  it  is  easier  and  gives  the  same  result.  Always 
indicate  the  multiplication  first  and  cancel  if  possible. 


WRITTEN   EXERCISE 


1.     |-|. 


2.   f-A. 


3.    A-l 


4. 

A-l- 

5. 

H-^l- 

6. 

-h^h 

7. 

t\-tV 

8. 

A-tV 

9. 

A-^V 

10. 

«-ii- 

11. 

T'^-f^ 

12. 

if-lf- 

13. 

il-H- 

14. 

il-li- 

15. 

A-3V 

16. 

¥-A- 

17. 

Tf?-M- 

18. 

Mf-H- 

19. 

m-i§- 

20. 

H-tIt- 

21. 

ill  -  H- 

22. 

Ht-A\- 

.23. 

m-Mi- 

24. 

iH-,V5 

26 


DIVISION 


21.  Dividing  mixed  numbers.    In  dividing  15j  by  7J,  we 

might 

1.  Reduce  to  a  common  denominator,  and  divide  the  new 
numerators.    -\^  -f-  ^^  =  62  ^  31  =  2.    Or 

2.  Multiply  both  dividend  and  divisor  by  a  common  denomi- 
nator, and  then  divide.  That  is,  15^  4-  7J  =  62  -j-  31,  by 
multiplying  by  4. 

But  practically  we 

3.  Reduce  to  fractional  forms  and  multiply  by  the  inverted 
divisor.     That  is,  15^  ^  7|  =  V 


-V=-¥-X/t  =  2. 


I.  21-31. 

4.  38 --5|. 

7.  59 -Sf. 

10.  33 -^7J. 

>^13.  12i 

16.  16| 

19.  15J-5J. 

22.  75-r-6TV 

.  91 


3i. 


WRITTEN   EXERCISE 

2.  83 --9f. 

5.  32 --4§. 

8.  41  --  85. 

11.  l^-^^. 

14.  15i  -r-  31. 

17.  61f--8i. 

-  20.  82  --  8t\. 


25.    51tV 

28.    31I-15H. 


12 
15 
18 
21 
24 
27 


3.  62 -f- 
6.  17 -f- 
9.  18|^ 
17i-f 
78- 
324- 
61|^ 

32  A 
62J- 


23.  27i-r-33j. 

26.  29j^59f. 

29.  13t«^^4|. 

^31.    776.5  -  129tV  32.  120tV -^- 14/^- *33.    62^^ 

/^    34.    How  many  strips  of  cloth,  each  5|  yd.  long, 
cut  from  a  strip  37|  yd.  long? 

^ —    35.    How  many  city  lots,  each  3l|  ft.  front,  can 
from  a  piece  having  222^  ft.  front  ? 

36.    How  many  yards  of  cloth  at  31^/  a  yard 
bought  for  a  dollar  and  a  half? 


5|. 

n- 

-2i. 

-n- 

-15i. 


30.    268-5-15,37. 

can  be 
be  cut 
can  be 


(^ 


GENERAL  PRINCIPLES  27 

GENERAL  PRINCIPLES  OF  THE  OPERATIONS 
ORAL   EXERCISE 

1.  If  I  put  4  ct.  with  3  ct.,  do  I  have  the  same  result  as 
if  I  put  3  ct.  with  4  ct.  ?  What  does  this  tell  about  the 
order  of  adding  numbers  ? 

2.  If  I  wish  to  add  4,  3,  and  5,  shall  I  get  the  same  result 
by  first  adding  4  +  3  and  then  5,  as  by  first  adding  3  +  5 
and  then  4  ?    What  does  this  tell  about  grouping  numbers  ? 

3.  How  does  3x4  compare  with  4x3?**** 
What  does  this  tell  about  the  order  of  multiply-  •  •  •  • 
ing  numbers  ?  •   •   ©   • 

22.  Law  of  order  .in  addition.  The  sum  is  the  same  what- 
ever the  order  of  the  addends. 

That  is,  2  +  3  =  3  +  2. 

23.  Law  of  grouping  in  addition.    The  sum  is  the  same 

however  the  addends  are  grouped. 
That  is,  (2  +  3)  +  5  =  2  +  (3  +  5). 

24.  Law  of  order  in  multiplication.  The  product  is  the 
same  whatever  the  order  of  the  factors. 

That  is,  2  X  3  =  3  X  2. 

WRITTEN   EXERCISE 

1.  Make  a  rectangle  |  in.  by  |  in.,  and  separate  it  into 
^-in.  squares,  and  show  that  5x3  =  3x5. 

2.  Show  that  (2  >^  3)  x  4  =  2  x  (3  x  4),  and  state  the 
law  of  grouping  in  multiplication. 

3.  We  have  found  that  2  +  3  =  3  + 2,  and  2x3  =  3x2. 
Does  2-f-3  =  3-T-2?   Write  out  a  statement  about  it. 


28  SHORT  METHODS 

THE  PRACTICAL  SHORT  METHODS 

25.  But  few  practical  short  methods.    There  are  many  short 
methods  of  operation,  and  of  these  a  few  are  really  prac- 
tical.    People  who  have  a 
great   amount  of   comput- 
ing now  use  machines,  just 

^^^^<#^'t^v^^^^^^^g|^|         as  those  who  have   much 

writing  to  do  now  use  a 
typewriter.  Here  is  a  pic- 
ture of  an  adding  machine 
such  as  is  used  by  most 
of  the  large  banks.  There 
are  also  machines  that 
multiply,  divide,  and  perform  other  operations. 

26.  Short  methods  in  addition.  1.  Learn  to  read  the  col- 
umns like  a  word,  without  pronouncing,  even  to  yourself, 
the  separate  numbers  any  more  than  necessary. 

2.  Accustom  yourself  to  "  catch  the  tens  ^'  as  much  as 
possible  in  adding.  Thus,  in  the  annexed  4- 
column,  the  eye  should  at  once  catch  the  two 
tens,  and  see  that  the  result  is  22.  There  is 
danger  of  mistakes  in  skipping  numbers  to 
catch  the  tens.  A  good  computer,  however, 
will  know  and  detect  the  other  combinations 
as  well  as  he  does  the  tens. 

3.  The  shortest  way  of  checking  the  work  is  to  add  in 
the  opposite  direction. 

4.  In  adding  several  long  columns,  keep  the  sums  of  each 
order  separate,  on  a  slip  of  paper,  and  add  these  partial 
sums.  At  least  keep  a  note  of  the  figures  "  carried."  This 
enables  you  to  check  more  readily. 


ADDITION     '  29 


ORAL   EXERCISE 


Look  at  the  example  and  state  only  the  sum : 
1.  17     2.  23     3.  42      4.  61      5.  15 
32       27       69        71        38 


6.  15  7.  21  8.  32 

13  12  14 

22  31  42 

11.  26  12.  33  13.  42 

25  12  63 

32  26  48 

16.  21  17.  32  18.  41 

35  76  88 

42  63  82 


21.  $75   22.  $31   23.  48  ft.   24.  29  in.   25.  32  yd. 
32       92      26        36        48 
61       86      35        27        62 


9. 

18 

10. 

21 

6 

10 

61 

73 

14. 

81 

15. 

16 

48 

17 

63 

82 

19. 

19 

20. 

28 

73 

29 

35 

46 

26.  $32   27.  $21   28.  36  yd.  29.  63  ft.   30.  81  lb. 
41       23      28        21        28 
62       49      42        42        96 


31.  $12   32.  $26   33.  26  lb.   34.  82  yd.   35.  29  ft. 
42       47      81        63        27 
37       35      29        48        36 


I 


30  SHORT  METHODS 

WRITTEN  EXERCISE 

See  how  long  it  takes  to  copy  these  numbers^  and  to  add 
and  check  each  result.      Write  the  time  with  the  results. 


13. 


$147.50 

2.  $748.06 

3.  $375.42 

4.  $298.04 

35.70 

126.53 

104.41 

127.63 

61.80 

39.40 

630.67 

701.96 

130.50 

86.51 

49.60 

872.37 

16.70 

28.42 

131.49 

286.32 

$359.68 

6.  $496.48 

7.  $396.04 

8.  $982.69 

298.76 

127.92 

72.63 

604.05 

400.92 

600.00 

129.87 

81.97 

640.32 

503.52 

871.64 

631.83 

701.24 

872.08 

280.93 

400.00 

248.72 

172.96 

371.40 

180.02 

9.  $1482.63    10.  $4761.42    11.  $3147.29     12.  $4268.75 


689.74 

3917.63 

2873.41 

3942.35 

2908.37 

5238.68 

4192.64 

2065.08 

8617.37 

6082.37 

128.46. 

6096.02 

9310.26 

4098.07 

3029.00 

2711.40 

7091.63 

5901.93 

7081.00 

1029.60 

328.04 

670.29 

283.96 

409.62 

127  ft.  9  in. 

14.    12  lb 

.  8  oz. 

.      15.    3yr 

.8: 

mo.  6  da. 

37       6 

9 

15 

5 

2 

27 

41       8 

17 

12 

3 

10 

14 

32       5 

15 

11 

1 

0 

19 

15       8 

21 

7 

3 

7 

0 

ADDITION  31 

16.  A  merchant  has  the  following  sums  owing  him : 
$147.60,  $21.30,  $29.47,  $63.82,  $173.46,  $391.14,  $2.94, 

$6  37,  $98.71.     What  is  the  total  amount? 

17.  What  was  the  total  number  of  dwellings  in  the  fol- 
lowing states  in  a  certain  year  ?  Illinois,  845,836 ;  Indiana, 
552,495 ;  Michigan,  521,648  ;  Missouri,  593,528 ;  New  York, 
1,035,180;  Ohio,  857,636;  Pennsylvania,  1,236,238 ;  Texas, 
575,734. 

18.  What  was  then  the  total  population  of  the  following 
cities  ?  New  York,  3,437,202  ;  Chicago,  1,698,575 ;  Philadel- 
phia, 1,293,697 ;  St.  Louis,  575,238  ;  Boston,  560,892  ;  Balti- 
more, 508,957;  Cleveland,  381,768;  Buffalo,  352,387;  San 
Francisco,  342,782 ;  Cincinnati,  325,902 ;  Pittsburg,  321,616. 

19.  What  was  then  the  total  number  of  school  children 
in  the  following  states  ?  Alabama,  733,222 ;  Arkansas, 
529,375;  Georgia,  885,725;  Illinois,  1,589,915;  Indiana, 
843,885;  Iowa,  767,870;  Kansas,  527,560;  Kentucky, 
798,027;  Louisiana,  538,267;  Massachusetts,  778,110; 
Michigan,  790,275 ;  Minnesota,  612,990 ;  Mississippi, 
633,026 ;  Missouri,  1,105,258  ;  New  Jersey,  572,923  ;  New 
York,  2,146,764  ;  North  Carolina,  753,826 ;  Ohio,  1,338,345  ; 
Pennsylvania,  2,031,171;  South  Carolina,  560,773;  Ten- 
nessee, 780,421;  Texas,  1,215,634;  Wisconsin,  730,685. 

20.  The  cost  of  some  of  our  largest  war  ships  is  as 
follows  :  Georgia,  $3,590,000  ;  Indiana,  $3,063,000  ;  Iowa, 
$3,010,000;  Massachusetts,  $3,063,000;  Nebraska,  $3,733,- 
600 ;  New  Jersey,  $3,405,000 ;  Oregon,  $3,222,810 ;  Rhode 
Island,  $3,405,000 ;  Virginia,  $3,590,000 ;  California,^ 
$3,800,000;  Colorado,  $3,780,000;  Maryland,  $3,775,000 
Pennsylvania,  $3,890,000;  South  Dakota,  $3,750,000 
West   Virginia,  $3,885,000.     What  is  their  total  cost? 


I 


32  SHORT  METHODS 

27.  Short  methods  in  subtraction.  The  shortest  plan  of 
subtraction  is  the  "  making  change  "  method.  It  is  better, 
however,  to  follow  the  method  with  which  the  class  is 
familiar.  All  work  should  be  checked  by  adding  the 
remainder  and  the  subtrahend,  the  sum  being  the  minuend. 

ORAL   EXERCISE 

Imagine  yourself  buying  goods  at  a  store^  and  handing 
the  clerk  the  first  amount  given^  the  goods  costing  the 
second  amount.    State  the  amount  of  change  due  you, 

1.    $1,  72/^.  2.    $2,  $1.37.  3.    $2,  $1.67. 

4.    $3,  $2.1T.  5.    $4,  $3.41.  6.    $5,  $1.27. 

7.    $5,  $2.40.  8.    $5,  $3.05.  9.    $5,  $1.70. 

10.    $10,  $6.55.        11.    $10,  $7.05.        12.    $10,  $6.05. 
13.    $10,  $5.70.        14.    $10,  $3.70.        15.    $10,  $8.67. 
16.    $15,  $12.75.      17.    $15,  $13.60.      18.    $15,  $11.42. 
19.    $20,  $16.92.     20.    $20,  $17.30.      21.    $20,  $16.05. 
22.    $25,  $19.60.     23.    $35,  $32.70.      24.    $40,  $37.06. 

25.  Subtract  78  from  the  sum  of  45  and  57. 

26.  Subtract  49  from  the  difference  between  37  and  88. 

27.  Subtract  the  difference  between  69  and  72  from  their 
sum. 

28.  The  difference  is  48  and  the  minuend  is  63.  What 
is  the  subtrahend? 

29.  How  much  less  is  the  difference  between  68  and  81 
than  that  between  49  and  68  ? 

30.  How  much  greater  is  the  difference  between  37  and 
64  than  that  between  37  and  19  ? 


SUBTRACTION  83 


WRITTEN  EXERCISE 


See  how  long  it  takes  to  copy  these  numbers^  and  to  sub- 
tract and  check.    Write  the  time  with  the  last  result, 

1.  $175.62        2.  $129.87        3.  $208.09         4.  $400.12 

81.98  67.98  98.78  69.84 

5.  $170.08    6.  $370.42   7.  $209.18    8.  $302.78 

69.99  91.64  87.69  62.95 


9.  $802.65  10.  $200.00  11.  $608.75  12.  $672.93 

69.81       93.74       35.82  98.94 

13.  $409.98  14.  $682.70  15.  $200.00  16,  $325.34 

23.49       93.81       187.60  128.92 

17.  $429.81  18.  $308.72  19.  $298.05  20.  $408.00 

149.92      129.85       109.72  129.60 

21.  $1087.50  22.  $2023.40  23.  $3029.62  24.  $3278.48 

963.90      1285.42      2172.58  1284.69 

25.  37  ft.  8  in.     26.  41  lb.  8  oz.    27.  39  yd.  9  in. 

29   9          29  12  27    16 


28.  9  mo.  8  da.  29.  12  yr.  4  da.  30.  6°  9'  21" 
6    15          8   92         1  27  42 

31.  15  mi.  125  ft.  32.  134  ft.  3  in.  33.  42°  6'  23" 
8    650       '  69   9         29  18  50 

34.  67  gal.  1  qt.  35.  5  yr.  2  mo.  36.  75°  18'  48" 
19    3         2    11         29  37  59 


34  SHORT  METHODS 

37.  A  man  deposited  $42.96  and  $125  in  a  bank,  and 
drew  out  $103.75.    How  much  was  left? 

38.  A  man  had  $287.50  in  a  bank,  and  he  drew  out 
$12.75  and  $37.63.    How  much  was  left? 

39.  A  man  deposited  $15  a  week  in  a  bank,  for  13 
weeks.  During  this  time  he  drew  out  $7.29,  $6.35,  $14.20, 
and  $5.75.    How  much  had  he  left  at  the  end  of  the  time  ? 

40.  In  a  year  when  this  country  produced  522,229,505 
bu.  of  wheat,  and  800,125,989  bu.  of  oats,  what  was  the 
difference  in  amount  ? 

41.  There  were  841,201,546  acres  of  farm  land  in  this 
country  in  a  certain  year,  414,793,191  being  improved. 
How  many  acres  were  unimproved  ? 

42.  Of  the  total  number  of  farms  in  this  country,  5,739,- 
657,  in  a  certain  year,  there  were  5,537,731  with  buildings 
on  them.    How  many  had  no  buildings  ? 

43.  The  value  of  this  farm  property  was  then  $20,514,- 
001,838,  of  which  $13,114,492,056  was  the  value  of  the 
land.  What  was  the  value  of  the  buildings,  implements, 
and  stock? 

44.  By  how  much  did  the  population  of  London,  4,536,- 
063,  in  a  certain  year,  exceed  that  of  New  York,  3,437,202  ? 
of  Chicago,  1,698,575  ?  of  Boston,  560,892  ? 

45.  When  the  irrigation  systems  of  California  had  cost 
$19,181,610,  and  those  of  Colorado  $11,758,703,  how  much 
more  had  California  spent  on  irrigation  than  Colorado  ? 

46.  The  states  having  the  greatest  railroad  mileage  in  a 
certain  year  were:  Illinois,  11,116.18  mi.;  Pennsylvania, 
10,480.35  mi. ;  and  Texas,  10,189.04  mi.  By  how  much 
did  that  of  Illinois  exceed  each  of  the  other  two? 


MULTIPLICATION  36 

28.  Short  methods  in  multiplication.  There  are  a  few  mul- 
tipliers which  are  used  so  frequently  in  business  that  it  is 
desirable  to  know  the  shortest  methods  of  multiplying  by 
them.  These  include  the  numbers  5, 10,  25,  125  (with  12.5 
or  12J),  33J,  and  their  various  per  cents,  together  with  9 
and  11. 

ORAL   EXERCISE 

1.  Multiply  by  10 :  43,  6.7,  0.42,  300,  $260.10. 

2.  State  the  short  method  of  multiplying  by  10. 

3.  Multiply  by  100 :   75,  8.2,  5.2,  $600,  $425.75. 

4.  State  the  short  method  of  multiplying  by  100. 

5.  Since  5  =  i.f ,  to  multiply  by  5  why  may  we  annex 


a  0,  or  move  the  decimal  point  one  place  to  the  right,  and 
then  ^ividebv  2  ?    Illustrate  by  an  example. 

6.  Multiply  by  5:  40,  66,  84,  98,  104,  124,  666,  42.2. 

7.  Since  25  =  i£5.^  what  is  the  short  method  of  multi- 
plying by  25  ?    Illustrate  by  an  example. 

8.  |Multiplyby25j  48,  64,  82,  34,  81, 13,  448,  204,  216. 

9.  Since|33^  =  J-§^,|what  is  the  short  method  of  multi- 
plying by  33J  ?    Illustrate  by  an  example. 

10.  Multiply  by  33j :    60,  36,  42,  51,  66,  123,  312,  111, 
66.3,  42.6,  15.63,  3.3333,  12,000,^  93,300,  690,000. 

11.  Since  |1 25  —  ^^^-^j  what  is  the  short  method  of  mul- 
tiplying by  125?    Illustrate  by  an  example. 

12.  Multiply  by  125  :  48,  56,  12,  36,  44,  8,  S.8,  4.8,  4.88, 
L688,  800,  8800,  1600,  16,000,  32,000. 

13.  50  X  44.  14.  50  X  68.  15.  50  x  124. 
16.  50  X  240.  17.  250  x  12.  18.  250  x  16. 
19.  250  X  24.  20.  250  x  40.  21.  125  x  16. 
22.    1250  X  16.         23.    1250  x  24.           24.    1250  x  32. 


86  SHORT  METHODS 

25.  Since  5%  =  yj^  =  t^,  to  multiply  by  6%  is  to  divide 
by  10  and  by  what  other  number  ?     Illustrate. 

26.  How  much  is  5%  of  40?  of  70?  of  90?  of  $230? 
of  $350?  of  400  ft.?  of  $2.60?  of  4220?  of  84,000? 

27.  Since  25  (^o  =  i?  what  is  the  short  method  of  finding 
25%  of  a  number?     Illustrate. 

28.  How  much  is  25%   of  620?   of  460?   of  $30?  of 
$924?  of  $424?  of  $4.32?  of  1600?  of  32,000? 

29.  Since  33^%  =  J,  what  is  the  short  method  of  find- 
ing 33  J  %  of  a  number?     Illustrate. 

30.  How  much  is  33  J  %  of  48?  of  $63?  of  $720?  of 
$1.23?  of  456  ft.?  of  1230  mi.?  of  72,000?  of  15.63? 

31.  Since  12^%  =  |,  what  is  the  short  method  of  find- 
ing 12^%  of  a  number?     Illustrate. 

32.  How  much  is  12^%  of  48?  of  56?  of  $720  ?  of  $6.40? 
of  800  ft.?  of  $1600?  of  72,000?  of  16.08? 

33.  Increase  $48  by  25%  of  itself. 

34.  Decrease  $800  by  5%  of  itself. 

35.  Increase  $160  by  12^%  of  itself. 

36.  Decrease  $720  by  33 J  %  of  itself. 

37.  What  will  125  erasers  cost  at  5/  each? 

38.  What  will  72  doz.  eggs  cost  at  12^/  a  dozen? 

39.  What  will  24  yd.  of  silk  cost  at  $1.25  a  yard? 

40.  What  will  36  yd.  of  cloth  cost  at  25/  a  yard? 

41.  What  will  16  yd.  of  cloth  cost  at  12J/  a  yard? 

42.  What  will  $8.40  worth  of  goods  cost  at  25%  off? 

43.  What  will  $3.60  worth  of  goods  cost  at  33^%  off? 

44.  Find  25%  of  331  %  of  12;  of  600  ;  of  1200 ;  of  1500. 

45.  Find  12i%  of  50%  of  16  ;  of  160  ;  of  1600  ;  of  4800. 

46.  Find  5%  of  10%  of  12i%  of  80;  of  1600;  of  3200. 


MULTIPLICATION  37 

,^^^9.    Summary  of  short  methods  of  multiplying. 

1.  To  TTiultiply  by  10,  move  the  decimal  point  one  place 
to  the  right,  annexing  zero  if  necessary, 

2.  To  multiply  by  100,  move  the  decimal  point  two  places 
to  the  right,  annexing  zeros  if  necessary, 

3.  T^  multiply  by  5,  multiply  by  10  and  divide  by  2. 

4.  To  multiply  by  25,  multiply  by  100  and  divide  by  4. 

5.  To  multiply  by  125,  multiply  by  1000  and  divide  by  8. 

6.  To  inultiply  by  33^^  multiply  by  100  and  divide  by  3. 

7.  To  find  h^^o,  divide  by  10  and  by  2.' 

8.  To  find  25%,  divide  by  4. -,  50%,  ^»?/  2  ;  20%,  by  5. 

9.  Tofind33\ofo,tci^e\',  66^%,  take  ^. 

10.  To  find  12J%,  ?^aA;6  ^  ;  16f  %,  25aA;e  ^.         ' 

11.  To  multiply  by  9,  which  is  10  —  1,  multiply  by  10 
and  then  subtract  the  multiplicand. 

Thus,  9  times  476  =  4760  -  476  =  4284. 

12.  To  multiply  by  11,  which  is  10  +  1,  multiply  by  10 
and  then  add  the  multiplicand. 

'       WRITTEN   EXERCISE 

1.  Multiply  by  125 :  4832,  5275,  6892,  $49,365. 

2.  Multiply  by  33J  :  1011,  7227,  3102,  $43,392. 
^  3.   Find  12^%  of  $6848,  $3272,  $42.48,  $35,284. 

4.  Find  16f  %  of  600,  $33.42,  $14,286.66,  $32,331.36. 

5.  Find  66f  %  of  $41.10,  $33.66,  $14,283.12,  $68,391.21. 
.  6.   Find  25%  of  33  J  %  of  12,  $298.32,  $3802.80,  $296.64. 

^  7.    Multiply  by  9  :  329,  746,  $981,  628  ft.,  1476,  $23,481. 
^  8.    Multiply  by  11:  6123,  3762,  $4837,  3972  ft.,  $31,287. 


38  SHORT  METHODS 


ORAL   EXERCISE 


Find  the  cost  of  the  following : 

Do  not  analyze  aloud,  at  least  until  after  the  answer  is  given. 
Use  short  processes  (page  37). 

1.  3j  yd.  of  felt  @  $1.60.  |^'^^ 

2.  16  yd.  of  denim  @  15/. 

3.  71  yd.  of  dimity  @  16/. 

4.  31  lb.  of  feathers  @  48/. 

5.  32  yd.  of  cambric  @  11/. 

6.  9  yd.  of  cashmere  @  75/. 

7.  16  yd.  of  gingham  @  11/. 

8.  22  yd.  of  buckram  @  15/. 

9.  17  yd.  of  crinoline  @  11/. 

10.  15  yd.  of  percaline  @  23/. 

11.  7  pieces  of  beading  @  23/. 

12.  8  yd.  of  eider  down  @  65/. 

13.  12  yd.  of  chambray  @  25/. 

14.  22J  yd.  of  nainsook  @  20/. 

15.  16  yd.  of  linen  lawn  @  75/. 

16.  A  dozen  whalebones  @  24/. 

17.  35  yd.  of  cheese  cloth  @  5/. 

18.  12  yd.  of  jute  burlap  @  35/. 

19.  3^  doz.  Clark's  cotton  @  42/. 

20.  7|  yd.  of  torchon  lace  @  12/. 

21.  4 J  doz.  basting  cotton  @  24/. 

22.  15  yd.  of  cotton  scrim  @  22/. 

23.  5^  doz.  darning  cotton  @  24/. 

24.  7*  gross  of  bone  buttons  @  22/. 


MULTIPLICATION  39 

25.  16  gross  of  shoe  buttons  @  7/. 

26.  8j  yd.  of  farmer's  satin  @  44/. 

27.  31^  yd.  of  damask  linen  @  98/. 

28.  5f  yd.  of  cotton  flannel  @  16/. 

29.  8  yd.  of  cotton  burlap  @  $1.12. 

30.  7^  lb.  of  hammock  cord  @  22/. 

31.  22j  yd.  of  Persian  lawn  @  30/. 

32.  11  yd.  of  striped  flannel  @  65/. 

33.  14  yd.  of  plain  gingham  @  25/, 

34.  15  pieces  of  mohair  braid  @  9/. 

35.  6  balls  of  crochet  cotton  @  35/. 

36.  8  pieces  of  seam  binding  @  12/. 

37.  19  skeins  of  Prisma  cotton  @  5/. 

38.  17J  yd.  of  butcher's  linen  @  50/. 

39.  15  yd.  of  huckaback  linen  @  45/. 

40.  17  yd.  of  unbleached  muslin  @  7/. 

41.  17  skeins  of  Poseidon  cotton  @  3/. 

42.  7  yd.  of  arras-cloth  burlap  @  $1.25. 

43.  16  yd.  of  Alpine  rose  muslin  @  9i/. 

44.  15  yd.  of  Java  cream  canvas  @  70/. 

45.  25  yd.  of  Java  colored  canvas  @  45/. 

46.  15  yd.  of  single-thread  canvas  @  60/. 

47.  11  yd.  of  white  narrow  canvas  @  38/. 

48.  9  yd.  of  basket-weave  burlap  @  $1.15. 

49.  ^  doz.  boxes  for  materials  @  35/  each. 

50.  A  gross  of  pearl  buttons  @  13/  a  dozen. 

51.  7  pieces  of  feather-stitched  braid  @  24/. 

52.  16  balls  of  knitting  cotton  @  4  for  a  quarter. 


40  SHORT  METHODS 

53.  If  6  lb.  of  coffee  cost  $1.86,  what  will  5  lb.  cost? 

54.  If  12  lb.  of  butter  cost  $3,  what  will  18  lb.  cost? 

55.  If  f  of  a  building  lot  is  worth  $2200,  what  is  the  lot 
worth  ? 

56.  At  $24  a  month,  what  is  the  rent  of  a  house  for 
3^  mo.? 

57.  If   3%    of   a  number  is   36,  what  is   5  times  the 
number  ? 

58.    If  7%  of  a  number  is  63,  what  is  20  times  the 

number  ? 

'  )  a^- 

59.  If  the  divisor  is  13  and  the  quotient  is  12,  what  is 
the  dividend  ? 

60.  If  a  man  buys  a  horse  for  $150  and  sells  it  at  an 
advance  of  30%,  what  is  the  selling  price? 

61.  A  grocer  bought  coffee  at  25/  a  pound  and  sold  it 
at  a  profit  of  20%.    What  was  the  selling  price? 

62.  If  a  man  can  build  a  fence  in  32  days,  in  how  many 
days  should  he  build  12  J  %  of  it? 

63.  The  product  of  three  numbers  is  242.    Two  of  the 
numbers  are  11  and  2.    What  is  the  third  number  ? 

64.  If  a  man  owned  |  of  the  stock  of  a  certain  company 
and  sold  f  of  his  share,  how  much  did  he  have  left?    3^ 

65.  A  man  buys  $11.88  worth  of  goods  and  sells  ^  of 
them  at  the  same  rate.     How  much  does  he  receive  ? 

66.  How  many  square  rods  are  there  in  a  field  20  rd. 
square?    What  is  the  land  worth  at  $|  a  square  rod? 


MULTIPLICATION  41 

State  the  profit  in  buying  the  following  goods  at  the  price 
first  given^  and  selling  at  the  second  price  : 

67.  12  lb.  mixed  caudy,  $1.92 ;  25/  a  pound. 

__68.  25  bars  peanut  brittle^  $1.56;  10/  ajbar./ 

69.  216  chocolate  bars,  45/ ;  3  bars  for  a  cent. 

70.  1  doz.  boxes  chocolate  chips,  $1.92;  25/  a  box.  i 

71.  6  lb.  fine  chocolate  creams,  $2.40;  60/  a  pound.  O-^ 

72.  75  packages  peanut  brittle,  $4.68;  10/  a  package.  ^"^"^ 

73.  40  packages  chocolate  drops,  $1.25  ;  5/  a  package. 

74.  12  packages  chocolate  creams,  72/  ;  10/  a  package. 

75.  2  boxes  chocolate  cream  bars,  48  to  the  box,  76/ ; 
1/  a  bar. 

76.  4  boxes  gum  drops,  24  packages  to  the  box,  $3 ;  5/ 
a  package. 

77.  3  boxes  caramels,  40  packages  to  the  box,  $3.75 ;  5/    ^''h^-^ 
a  package.  ■H-ji^^'Ji— 

78.  5  boxes  licorice  drops,  48  packages  to  the  box,  $7.20 ; 
5/  a  package. 

79.  4  boxes  chocolate  almonds,  40  packages  to  the  box, 
$5  ;  5/  a  package. 

80.  9  cases  lemon  soda,  2  doz.  bottles  to  the  case,  $4.50 ; 
5/  a  bottle. 

81.  6  boxes  salted  peanuts,  24  packages  to  the  box,  75/ 
a  box;  5/  a  package. 

82.  4  boxes  pepsin  chewing  gum,  20  packages  to  the  box, 
$2.20;  5/  a  package. 

83.  3  boxes  vanilla  chocolates,  2  doz.  packages  to  the 
box,  $2.25  ;  5/  a  package. 


42  SHORT  METHODS 

30.  Short  methods  in  division.  There  are  a  few  divisors 
which  are  used  so  frequently  in  business  that  it  is  desir- 
able to  know  the  shortest  methods  of  dividing  by  them. 
These  include  the  numbers  5,  10,  25,  100,  125  (with  12.5 
or  12^),  and  33J. 

ORAL   EXERCISE 

1.  Divide  by  10  :  $420,  $5700,  330,  $425,  375  lb.,  6  mi. 

2.  State  the  short  method  of  dividing  by  10. 

3.  Since  J  =  ^q,  we  may  take  J  of  a  dollar  by  taking 
how  many  tenths  of  it  ?  State  a  short  method  of  dividing 
by  5,  or  of  taking  ^^  of  a  number. 

4.  Divide  by  5  :  $1110,  $3240,  5280  ft.,  4230  mi.,  3221. 
.5.    Divide  by  100:  $600,  7000,  4800,  $560,  $275,  $48. 

6.  State  the  short  method  of  dividing  by  100. 

7.  State  the  short  method  of  finding  ^^  (qr  y^^)  of  a 
dollar;  of  dividing  a  number  by  25. 

8.  Divide  by  25 :  $2200,  $1200,  $3100,  4100,  $32,  $11. 

9.  State  the  short  method  of  dividing  by  125.    (j^^  = 

tA(T-) 

10.  DivideJjyjL25 :  $11,000,  2000,  $4000,  $70,  $600. 

11.  State  the  short  method  of  dividing  by  33 J.    (Take 

t8o-)  ^    ^     ^''^''^\'.:^         ^^   ^v^--  ^    ■}.-.. 

12.  Divide  by  33i :  $200, 500,  |7,  $12,  $30,000,  $11,000. 

13.  In  a  certain  year  Delaware  had  346.2  mi.  of  railroad, 
and  the  District  of  Columbia  had  yi^  ^s  many.  How  much 
had  the  latter? 

14.  France  then  had  26,600  mi.  of  railroad,  and  Korea 
had  0.001  as  many.    How  many  had  Korea? 

15.  The  United  States  then  had  193,300  mi.  of  railroad, 
and  Ecuador  had  0.001  as  many.    How  many  had  Ecuador? 


DIVISION  43 

31.  Summary  of  short  methods  of  division. 

1.  To  divide  hy  10,  Tnove  the  decimal  point  one  place  to  the 
left. 

2.  To  divide  by  100,  move  the  decimal  point  two  places  to 
the  left,  and  so  on  for  other  powers  of  10. 

3.  To  divide  hy  S,  multiply  by  2  and  divide  by  10.  y 

4.  To  divide  by  25,  multiply  by  4  and  divide  by  100. 

5.  To  divide  by  125,  multiply  by  8  and  divide  by  1000. 

6.  To  divide  by  33 J,  multiply  by  3  and  divide  by  100.  •^■" 

WRITTEN   EXERCISE 

1.  State  a  short  method  of  dividing  by  66f ,  or  ^§5.. 

2.  State  a  short  method  of  dividing  by  16f ,  or  if  ^. 

3.  State  a  short  method  of  dividing  by  12j,  or  -i-§^. 

4.  6484 --66f.        5.    7280-^66f. 
7.  2937  ^16f.        8.    4831-r-16f. 

10.  9237^121.      11.    7396-^12i. 

13.  6889 -^33J.      14.   4959-- 331. 

16.  4936^125.      17.   67,400-- 125. 

19.  Divide  by  25  :  13,428,  $37,642,  $135,621,  $427,693. 

20.  Divide  by  125  :  17,200,  $68,300,  $276,400,  $317,500. 

21.  Divide  by  33J  :  69,720,  $32,960,  $48,750,  $276,320. 

22.  At  25/  a  yard,  how  many  yards  of  cloth  can  be 
bought  for  $37.25? 

23.  At  33 J/  a  yard,  how  many  yards  of  cloth  can  be 
bought  for  $98? 

24.  Divide  3,742,697  by  25,  by  long  division,  and  see 
how  many  seconds  it  takes.  Do  the  same  by  the  short 
method  §tated  ^bpve.    Write  the  time  with  the  answer. 


6. 

9276- 

-66|. 

9. 

9134- 

-16f. 

12. 

8187 -V 

■12i. 

15. 

8892- 

•33J. 

18. 

39,888 

-f-125. 

44  SHORT  METHODS 

ORAL   EXERCISE 

1.  To  multiply  by  ^  is  the  same  as  to  divide  by  what 
number?  To  divide  by  ^  is  the  same  as  to  multiply  by 
what  number?    Illustrate  on  the  blackboard. 

2.  Multiply  by  i :  48,  250,  380,  460,  666,  1110,  1234. 

3.  Divide  by  J:  70,  35,  60,  300,  450,700,  1450,  8112. 

4.  To  multiply  by  J  is  the  same  as  to  divide  by  what 
number?  To  divide  by  ^  is  the  same  as  to  multiply  by 
what  number?    Illustrate  on  the  blackboard. 

5.  Multiply  by  ^:  36,  90,  63,  45,  75,  300,  123,  321. 

6.  Divide  by  J  :  30,  70,  50,  25,  80,  400,  2000,  4211. 

7.  Multiply  by  f :  30,  60,  90,  33,  63,  300,  600,  1230. 

8.  Divide  by  f :  20,  12,  16,  10,  60,  100,  200,  500,  1000. 

9.  Multiply  by  i:  8,  16,  32,  48,  64,  84,  100,  200,  1000. 

10.  Divide  by  i :  9,  11,  21,  25,  60,  70,  91, 125,  250,  800. 

11.  Multiply  by  |:  8,  16,  20,  32,  40,  44,  48,  60,  80,  444. 

12.  Divide  by  |:  9,  12,  15,  21,  30,  60,  66,  90,  120,  300. 

13.  Since  ^  =  j^^,  what  is  the  short  method  of  multi- 
plying by  i?  of  dividing  by  J? 

14.  Multiply  by  ^ :  21,  31,  34,  123,  112,  321,  132,  125. 

15.  Divide  by  i:  22,  300,  34,  160,  444,  664,  486,  1010. 

16.  Since  f  =  .4,  state  a  short  method  of  multiplying  and 
of  dividing  by  f .    Do  the  same  for  f  and  J. 

17.  Multiply  by  f:  30,  60,  66,  120,  600,  720,  840,  1200. 

18.  Because  .12^  =Jj  what  is  the  short  method  of  multi- 
plying by  .12^  ? 

19.  At  12^/  a  yard,  what  will  16  yd.  cost?  72  yd.? 


BUSINESS  FRACTIONS  45 

20.  At  48/  a  dozen,  what  will  ^  doz.  eggs  cost  ? 

21.  At  $1.28  a  yard,  what  will  |  yd,  of  silk  cost? 

22.  At  $1.20  a  yard,  what  will  |  yd.  of  silk  cost? 

23.  At  $2.40  a  yard,  what  will  |  yd.  of  lace  cost  ? 

24.  At  $1.68  a  yard,  what  will  j  yd.  of  lace  cost? 

25.  At  78/  a  yard,  what  will  J  yd.  of  velvet  cost  ? 

26.  At  $18.60  a  dozen,  what  will  §  doz.  spoons  cost  ? 

27.  At  12 J/  a  yard,  how  much  cloth  will  $1.50  buy? 

28.  How  much  will  12j  doz.  forks  cost  at  $16  a  dozen  ? 

29.  How  much  will  6J  doz.  eggs  cost  at  16/  a  dozen  ? 

30.  At  16/  a  pound,  how  much  will  3 J  lb.  of  meat  cost? 

31.  At  24/  a  pound,  how  much  will  2 1  lb.  of  meat  cost? 

32.  At  64/  a  pound,  what  will  |  lb.  shelled  almonds 
cost  ?    What  will  2  lb.  4  oz.  cost  ? 

33.  At  36/  a  dozen,  how  much  must  a  dealer  pay  for 
2 J  doz.  small  bottles  of  mucilage  ? 

34.  At  $19.20  a  dozen,  how  much  must  a  dealer  pay  for 
Ij  doz.  fountain  pens ?  for  2  doz.? 

35.  At  15  mi.  an  hour,  how  far  will  an  automobile  travel 
in  20  min.  ?  in  40  min.  ?  in  30  min.  ? 

36.  At  12j/  a  dozen,  how  many  dozen  eggs  will  $9.25 
buy  ?    How  many  dozen  will  $12.50  buy  ? 

37.  At  35  mi.  an  hour,  how  far  will  a  train  travel  in 
12  min.  ?  in  24  min.?  in  36  min.?  in  48  min.? 

38.  At  47  mi.  an  hour,  how  far  will  a  train  travel  in 
12  min.?    (12  min.  =  J  hr.)    How  far  in  15  min.  ? 


46  SHORT  METHODS 

WRITTEN   EXERCISE 

1.  1  of  $73.10.            2.  i  of  3§.            3.  i  of  375  ft. 

4.  1  of  $61.20.           5.  1  of  5J.            6.  1  of  239  ft. 

7.  J  of  $27.40.            8.  I  of  6|.            9.  f  of  297  lb. 

10.  J  of  $71.40.          11.  i  of  4J.           12.  J  of  237  yd. 

13.  2  of  $62.10.          14.  f  of  2§.           15.   2  of  128  mi. 

16.  J  of  $67.30.         .17.  f  of  42.           18.  f  of  293  yd. 

/  19.  123  X  16*.             20.  321  X  631.  ^21.  41f  x  33i. 

22.  121%  of  $72.40.^^3.  121%  of  61.  24.  12i%of375ft. 

x25.  275  in.  --  i  in.                   26.    268  ft.  -f- 1  ft. 

27.  826  yd.  --  i  yd.                 28.    2372  ft.  --  J  ft. 

29.  1635  yd.  ~  i  yd.              30.    $12.60  --  $0.12i. 

31.  $32.40  -^  $0,121              32.    268  yd.  --  12^  yd. 

,    33.  At  121/  a  yard,  how  much  cloth  will  $876  buy? 

34.  At  121/  a  gross,  how  many  gross  of  paper  fasteners 
will  $17.75  buy? 

35.  At  33J/  a  hundred,  how  many  photograph  cards  can 
be  bought  for  $1.83? 

36.  At  66^ j^  a  gross,  how  many  gross  of  pens  can  be 
bought  for  $24? 

37.  At  I  yd.  each,  how  many  strips  of  ribbon  can  be  cut 
^  from  a  piece  27  yd.  long? 

38.  When  a  train  is  traveling  at  the  rate  of  32  mi.  in  40 
min.,  what  is  its  rate  per  hour? 

^^^3d.   When  a  horse  is  trotting  at  the  rate  of  J  mi.  in 
3  min.,  what  is  his  rate  per  hour  ? 


MEASURES  47 

MEASURES 

32«  Tables  for  reference.    Although  these  tables  have  been 
learned,  they  are  here  inserted  for  reference  and  review. 

Table  of  Length 


fZ  feet  -  1  yardTyg;)^ 


5|  yards  or  16|  feet  =  1  rod  (rd.), 
320  rods  or^280  feet  =  Fmile  (mi.). 

The  hand  (4  in.)  is  used  in  measuring  the  height  of  horses  at 
the  shoulder.  Sailors  use  the  fathom  (6  ft.)  and  cable  length 
(120  fathoms)  for  measuring  depths,  and  the  knot  (nautical  mile, 
1.15  common  or  statute  miles,  or  6080.27  ft.)  for  distances.  A 
furlong  is  \  mi.,  a  league  is  3  mi.,  and  a  cubit  is  18  in. 

TA:eLE  OF  Square  Measure 

144  square  inches  (sq.  in.)  =  1  square  foot  (sq.  ft.). 
9  square  feet  =  1  square  yard  (sq.  yd.). 
30|  square  yards  =  1  square  rod  (sq.  rd.). 
160  square  rods  =  1  acre  (A.). 

640  acres  =  1  square  mile  (sq.  mi.). 

Carpenters,  architects,  and  mechanics  often  write  8''  for  8  in., 
and  5'  for  5  ft.     In  this  book  both  of  these  forms  are  used. 

Table  of  Cubic  Measure 

1728  cubic  inclies  (cu.  iiu)  =  1  cubic  foot  (cu.  ft.). 
27  cubic  feet  =  1  cubic  yard  (cu.  yd.). 
128  cubic  feet  =  1  cord  (cd.). 

A  perch  of  stone  or  masonry  is  usually  considered  as  1  rd.  long, 
1  ft.  high,  and  1|  ft.  thick,  and  it  contains  24 1  cu.  ft.  It  varies, 
however.    A  cubic  yard  of  earth  is  considered  a  load. 


48  MEASURES 

Table  of  Weight 

16  ounces  (oz.)  =  1  pound  (lb.). 
2000  pounds  =  1  ton  (T.). 

The  ton  of  2000  lb.  is  sometimes  called  the  short  ton,  there 
being  a  long  ton  of  2240  lb.  which  is  used  in  some  wholesale  trans- 
actions in  mining  products.    A  hundredweight  (cwt.)  is  100  lb. 

Goldsmiths  still  use  an  old  table  of  Troy  weight,  and  it  is  here 
inserted  for  reference.    In  this  table 

24  grains  (gr.)  =  1  pennyweight  (pwt.  or  dwt.). 
20  pennyweights  =  1  ounce  (oz.). 
12  oz.  =  1  pound  (lb.). 

The  avoirdupois  pound  contains  7000  gr.,  the  Troy  pound  5760  gr. 
Therefore  1  lb.  of  iron  is  heavier  than  1  lb.  of  gold. 

A  carat  weight,  used  in  weighing  diamonds,  varies,  but  is  commonly 
taken  in  the  United  States  as  3.2  Troy  grains.  The  word  carat  is 
also  used  in  speaking  of  the  purity  of  gold,  meaning  25,  "  16  carats 
fine  "  meaning  if  pure  gold. 

There  is  also  a  table  of  Apothecaries^  weight-,  used  by  physicians 
and  druggists  in  prescriptions.    It  is  here  inserted  for  reference. 

20  grains  (gr.)  =  1  scruple  (sc.  or  B). 
3  scruples  =  1  dram  (dr.  or  3). 
8  drams  =  1  ounce  (oz.  or  § ). 
12  ounces  =  1  pound  (lb.). 

Table  of  Liquid  Measure 

4gms(gi.)=lpint(pt.). 
2  pints  =  1  quart  (qt.). 
4  quarts  =  1  gallon  (gal.). 

A  gallon  contains  231  cu.  in.  Barrels  (bbl.)  vary  in  size,  although 
in  estimating  the  capacity  of  tanks  and  cisterns  31.5  gal.  are  con- 
sidered a  barrel,  and  2  bbl.  a  hogshead. 

There  is  also  a  table  of  Apothecaries'  liquid  measure,  in  which 
16  fluid  ounces  make  1  pint. 


TABLES  49 

Table  of  Dry  Measure 

2  pints  (pt.)  =  1  quart  (qt.). 
8  quarts  =  1  peck  (pk.). 
4  pecks  =  1  bushel  (bu.). 

A  bushel  contains  2150.42  cu.  in.  The  dry  quart  contains  67.2 
cu.  in.,  the  liquid  quart  only  57.75  cu.  in. 

Table  of  Time 

60  seconds  (sec.)  =  1  minute  (min.). 
60  minutes  =  1  hour  (hr.) . 
24  hours  =  1  day  (da.). 
7  days  =  1  week  (wk.). 
12  months  (mo.)  =  1  year  (yr.). 

"  Thirty  days  hath  September, 
April,  June,  and  November." 

The  other  months  have  31  days,  except  February,  which  has 
28  days  in  common  years  and  29  days  in  leap  years.  The  com- 
mon year  has  365  days,  or  52  weeks  and  1  day;  the  leap  year 
366  days.    A  century  is  100  years. 

Table  of  Value 

10  mills  (m.)  =  1  cent  (ct.  or  ^). 
10  cents  =  1  dime  (d.). 
10  dimes  =  1  dollar  ($). 

The  term  eagle  (for  ^10)  is  no  longer  used.   The  mill  is  not  coined. 

Arc  and  Angle  Measure 

60  seconds  (60")  =  1  minute  (1^. 
60  minutes  =  1  degree  (1°) . 
360  degrees  =  1  circumference. 

In  measuring  angles  360°  =  4  right  angles. 


60  MEASURES 

ORAL   EXERCISE 

1.  Express  640  rd.  as  miles. 

2.  Express  64  oz.  as  pounds. 

3.  Express  2  A.  as  square  rods. 

4.  Express  33  ft.  as  rods ;  as  yards. 
6.  Express  54  cu.  ft.  as  cubic  yards. 

6.  Express  9  ft.  as  inches  ;  as  yards. 

7.  Express  11  da.  as  hours ;  as  weeks. 

8.  Express  17  qt.  as  pints ;  as  gallons. 

9.  Express  9  pk.  as  quarts ;  as  bushels. 

10.  How  many  cubic  inches  in  10  cu.  ft.  ? 

11.  How  many  rods  in  3  mi.  ?    in  10  mi.? 

12.  How  many  yards  in  8  rd.?    in  10  rd.  ? 

13.  How  many  cubic  feet  in  2  cd.  of  wood? 

14.  Express  300  min.  as  hours ;  as  seconds. 

15.  How  many  quarts  in  a  barrel  of  31^  gal.? 

16.  How  many  pints  in  a  60-gallon  hogshead? 

17.  Express  80  sq.  rd.  as  a  fraction  of  an  acre. 

18.  How  many  right  angles  in  270°?    in  180°? 

19.  How  many  days  from  May  23  to  June  25? 

20.  How  many  days  from  June  11  to  July  17? 

21.  What  part  of  a  16-carat  ring  is  pure  gold? 

22.  Express  11  yd.  as  rods ;  as  feet ;  as  inches. 

23.  Express  30  pt.  as  quarts  ;  as  gills  ;  as  gallons. 

24.  How  many  feet  in  2  rd.  8  ft.?    in  2  rd.  10  ft.? 

25.  How  many  feet  in  10  rd.?    in  5  rd.  ?    in  2  rd.? 

26.  How  many  degrees  in  540'?    in  420'?    in  660'? 


REDUCTIONS  51 

27.  How  many  mills  in  $2.75  ? 

28.  How  many  days  from  August  15  to  October  15? 

29.  How  many  acres  in  a  tract  of  land  10  mi.  square  ? 

30.  How  many  days  from  January  17  to  February  17? 

31.  How  many  square  feet  in  10  sq.  yd.  ?    in  5  sq.  yd.  ? 

32.  At  6  qt.  a  day,  how  long  will  3  bu.  of  oats  last  a  horse  ? 

33.  What  is  the  perimeter  of  a  square  that  is  4  ft.  9  in. 
on  a  side  ? 

34.  What  is  the  side  of  a  square  whose  perimeter  is 
14  ft.  4  in.? 

35.  Since  a  gallon  contains  231  cu.  in.,  how  many  gallons 
in  693  cu.  in.? 

36.  How  many  square  feet  in  a  surface  having  an  area 
of  720  sq.  in.  ? 

37.  Express  a  long  ton  as  a  short  ton  and  hundredths 
of  a  short  ton. 

38.  What  is  the  perimeter  of  an  equilateral  triangle  that 
is  3  ft.  8  in.  on  a  side  ? 

39.  If  school  closes  June  21,  how  many  days  from  that' 
day  to  the  fourth  of  July  ? 

40.  How  many  quarts  will  a  lO-bushel  bin  hold?  a 
5-bushelbin?    How  many  pecks  in  each? 

41.  A  man  buys  a  building  lot  2  rd.  front.  How  many 
square  feet  of  sidewalk  5  ft.  wide  must  he  have  ? 

42.  A  cellar  13^  ft.  by  20  ft.  is  to  be  excavated  to  a  depth 
of  6  ft.  How  many  loads  (cubic  yards)  of  earth  must  be 
removed  ? 

43.  If  a  man  buys  a  load  of  coal  weighing  1  T.  600  lb., 
how  many  pounds  does  he  buy  ?  Express  this  in  tons  and 
tenths  of  a  ton. 


62  MEASURES 

33.  Illustrative  problems.     1.  Express  35J  yd.  as  feet. 
Since  1  yd.  =  3  ft., 

351  yd.  =  35^  times  3  ft.,  or  106  J  ft. 

2.  Express  81  oz.  as  pounds  and  ounces. 

Since  1  oz.  =  j\  lb., 

81  oz.  =  81  times  jV  lb.  =  6j\  lb.,  or  5  lb.  1  oz. 

3.  Express  2  ft.  8  in.  as  inches. 

Since  1  ft.  =  12  in., 

2  ft.  =  2  times  12  in.  =  24  in. 
2  ft.  8  in.  =  24  in.  +  8  in.  =  32  in. 

WRITTEN   EXERCISE 

1.  Express  92  rd.  3  ft.  as  feet ;  as  inches. 

2.  Express  32  yd.  2  ft.  as  feet ;  as  inches. 
-"^3.    Express  3^  A.  as  acres  and  square  rods. 

4.  Express  21  sq.  ft.  82  sq.  in.  as  square  inches. 

5.  Express  95  cu.  ft.  as  cubic  yards ;  as  cubic  inches. 
->_6.    Express  27  sq.  rd.  4  sq.  yd.  as  square  yards;  as  square 

•feet. 

7.    Express  8  sq.  yd.  7  sq.  ft.  as  square  feet;  as  square 

inches. 
-—  8.    Express  35  cu.  yd.  15  cu.  ft.  as  cubic  yards ;  as  cubic 

feet ;  as  cubic  inches. 

9.    Express  4  T.  1735  lb.  as  tons  and  the  decimal  part 

of  a  ton  ;  as  pounds  ;  as  ounces. 

^  10.    Express  39,426  lb.  as  tons  and  the  decimal  part  of  a 

ton ;  as  tons  and  pounds  ;  as  ounces. 
/  11.    Express  27  qt.  1  pt.  as  gallons  and  the  decimal  part 

of  a  gallon ;  as  quarts  and  the  decimal  part  of  a  quart ;  as 

pints. 


TABLES  63 

34.  Surveyors*  table  of  length  : 

7.92  inches  =  1  link  (li.). 
100  links  =  4  rods  =  1  chain  (ch.). 
80  chains  =  5280  ft.  =  1  mile. 

City  property  is  usually  measured  by  feet  and  decimal  fractions 
of  a  foot;  farm  property,  by  rods  or  chains. 

WRITTEN   EXERCISE 

1.  Express  1  mi.  as  chains ;  as  rods ;  as  links. 

2.  Express  142  ch.  as  miles  and  chains ;  as  rods. 

3.  Express  17  rd.  as  chains;  as  links;  as  inches. 

4.  How  many  feet  in  60  li.?    inlOch.?    in  125  li.? 

5.  Express  17  mi.  32  ch.  as  miles  and  the  decimal  part 
of  a  mile ;  as  chains  ;  as  rods. 

6.  It  is  30  ch.  44  li.  around  a  square  field.    How  long  is 
each  side?     Suppose  it  were  97  ch.  64  li.  around? 

^^  7.    An  equilateral  triangle  is  4.72  ch.  on  a  side.     How 
many  links  in  the  perimeter  ?     How  many  chains  ? 
^  8.    By  using  the  surveyors'  table,  find  how  many  inches 
there  are  in  a  mile.     Check  by  using  the  common  table. 

Add: 
9.   4  ch.  3  rd.         10.    38  ch.  93  li.       11.    9  mi.  275  rd. 
^92  19        78  8         192 


Subtract  : 

12.    26  ch.  1  rd. 

13.    19  ch.  15  li. 

14.    16  mi.  12  rd. 

17         3 

13        87 

7       234 

Multiple/  : 

15.    4  ch.   2  rd. 

16.    29  ch.  78  li. 

17.    8  mi.  192  rd. 

27 

16 

37 

54  MEASURES 

35.  Surveyors'  table  of  square  measure : 

16  sq.  rd.  =  1  square  chain  (sq.  ch.). 
10  sq.  ch.  =  1  acre  (A.). 

The  square  rod  is  sometimes  called  a  perch.  The  word  rood  is 
sometimes  met  in  reading,  meaning  40  sq.  rd.  or  \  acre.  640 
acres  =  1  sq.  mi.,  and  36  sq.  mi.  =  1  township  in  the  government 
surveys. 

ORAL   EXERCISE 

1.  Add  6  ch.  2  rd.  and  3  ch.  3  rd. 

2.  Express  3  A.  as  square  chains. 

3.  From  7  ch.  subtract  4  ch.  2  rd. 

4.  From  5  ch.  subtract  1  rd.  40  li. 

5.  Add  7  ch.  90  li.  and  6  ch.  70  li. 

6.  Express  2  mi.  as  rods ;  as  chains. 

7.  Multiply  1  ch.  2  rd.  by  2;  by  3;  by  4. 

8.  Express  as  square  rods :  3  sq.  ch.,  5  sq.  ch. 

9.  How  many  acres  in  30  sq.  ch.  ?    50  sq.  ch.  ? 

10.  How  many  square  chains  in  7  A.  ?  in  17  A.  ? 

11.  How  many  feet  in  10  mi. ?    How  many  chains? 

12.  Express  as  rods :  3  ch.,  5  ch.,  7  ch.,  16  ch.,  30  ch. 

13.  How  many  square  chains  in  a  field  6  ch.  by  9  ch.? 
How  many  acres? 

14.  How  many  square  chains  in  a  field  15  ch.  by  11  ch.? 
How  many  acres  ? 

15.  How  many  square  chains  in  a  field  5  ch.  by  4  ch.  ? 
How  many  acres  ? 

16.  Divide  15  ch.  by  2,  expressing  the  result  as  chains ; 
as  rods ;  as  chains  and  rods. 


AREAS  55 

36.  Illustrative  problem.    How  many  acres  in  a  field  32  ch. 
long  and  6  ch.  30  li.  wide  ? 

6  ch.  30  li.  =  6.30  ch. 
32  times  6.30  times  1  sq.  ch.  =  201.6  sq.  ch. 
Since  1  sq.  ch.  =  ^i^  A., 

201.6  sq.  ch.  =  201.6  times  ^V  A.  =  20.16  A. 

Actual  measurements  of  this  kind  in  connection  with  the  school 
ground  and  other  pieces  of  land  are  valuable. 

WRITTEN  EXERCISE 

Find  the  areas  in  acres : 

1.  16  ch.  by  14  ch.  2.    8  ch.  by  23  ch. 

3.  23  ch.  by  29  ch.  4.    32  ch.  by  34  ch. 

5.  5  ch.  2  rd.  by  11  ch.         6.    1  ch.  1  rd.  by  2  rd. 

7.  5  ch.  30  li.  by  17  ch.        8.    6  ch.  48  li.  by  9  ch. 

9.  6  ch.  80  li.  by  13  ch.      10.    5  ch.  18  li.  by  ^  ch. 

11.  8  ch.  10  li.  by  2^  ch.     12.    8  ch.  42  li.  by  12  ch. 

13.  11  ch.  75  li.  by  6  rd.     14.    8  ch.  30  li.  by  10  ch.  40  li. 

15.  12  ch.  45  li.  by  15  ch.  75  li. 

(    16.  13  ch.  80  li.  by  14  ch.  ^6  li. 

17.  32  ch.  75  li.  by  27  ch.  50  li. 

/IS.  27  ch.  42  li.  by  31  ch.  60  li. 

19.  34  ch.  27  li.  by  42  ch.  83  li. 

20.  14  ch.  15  li.  by  13  ch.  17  li. 

21.  Express  1  A.  as  square  yards  ;  as  square  feet. 

22.  Express  1  sq.  rd.  as  square  feet ;  as  square  inches. 

23.  Express  1  sq.  mi.  as  square  rods ;  as  square  yards ; 
as  square  feet. 

/  24.    Express  3  sq.  mi.  32  A.  as   square   miles  and  the 
decimal  part  of  a  square  mile  j  as  acres. 


56 


MEASURES 


r 


X 

15  ch. 

f/ 

.c 

R 

« 

(N 

30  ch. 

25.  Express  7  A.  8  sq.  ch.  as  acres  and  the  decimal  part 
of  an  acre ;  as  square  chains ;  as  square  rods. 

26.  How  many  square  feet  in  a  city  lot  31.8  ft.  wide  by 
107.6  ft.  long  ? 

27.  What  is  the  difference  in  area  between  a  piece  of 
ground  20  rd.  square  and  one  containing 
20  sq.  rd.? 
'   28.    In  the  field  here  shown  find  the 

length  of  X  and  y ;  the  perimeter ;  the 
number  of  acres. 

29.  How  many  square  feet  in  a  school  playground  8|-  rd. 
wide  and  160  ft.  long  ? 

30.  A  piece  of  land  34  ch.  by  15  ch.  is  sold  for  $75  an 
acre.    What  is  the  price  ? 

31.  Which  costs  the  more,  a  piece  of  land  42  ch.  by 
27  ch.  at  %^h  an  acre,  or  a  piece  37  ch.  by  29  ch.  at 
an  acre  ?    How  much  more  ? 

32.  In  the 
field  here  shown 
find  the  length 
of  X  and  y ;  the 
perimeter ;  the 
number  of  acres. 

^  33.  Two  fields  have  equal  perimeters,  80  ch.  One  is  a 
square  and  the  other  a  rectangle  30  ch.  long.  Having  equal 
perimeters,  have  they  equal  areas  ?  What  is  the  area  of  each  ? 

Find  the  value  of  the  following  pieces  of  land: 

34.  24  ch.  by  30  ch.  at  $75  an  acre. 

35.  42  ch.  by  ^^  ch.  50  li.  at  $85  an  acre. 

36.  37  ch.  50  li.  by  42  ch.  75  li.  at  $60  an  acre. 


X 

20  ch. 

y 

10  ch. 

■§ 

o 

50  ch. 

2 

/ 


AREAS 


67 


ORAL   EXERCISE 

1.    If  a  rectangle  lias  an  area  of  50  sq.  in.,  and  is  10  in. 
long,  how  wide  is  it  ?     What  is  its  perimeter  ? 

State  only  the  answers  on  this  page.     Reserve  explanations  for 
written  work. 

State  the  lengths  of  rectangles  whose  areas  and  widths 
are  as  follows: 


3.  if  sq.  in.,  |  in. 

5.  45  sq.  rd.,  5  rd. 

7.  54  sq.  ch.,  6  ch. 

9.  143  sq.  in.,  11  in. 

11.  750  sq.  in.,  20  in. 


OT     100  ft. 


2.  72  sq.  ft.,  8  ft. 

4.  ^5^  sq.  in.,  f  in. 

6.  5Q  sq.  ch.,  7  ch. 

8.  132  sq.  ft.,  11  ft. 

10.  108  sq.  ch.,  9  ch. 

12.  How  many  square  feet  in  the 
area  of  this  city  lot  ?  (Take  the  parts 
on  opposite  sides  of  the  dotted  line, 
find  the  area  of  each  separately,  and 
add.) 

13.  Find  the  areas  of  squares  whose  sides  are  6  in., 
12  in.,  4  in.,  11  in.,  20  in.,  40  in.,  100  in. 

14.  A  square  has  an  area  of  25  sq.  in.     What  is  the 
length  of  each  side  ? 

State  the  lengths  of  the  sides  of  squares  whose  areas  are 
as  follows  : 

15.  49  sq.  ch.  16.  81  sq.  ft.  17.  64  sq.  in. 
18.  100  sq.  mi.  19.  144  sq.  in.  20.  121  sq.  ft. 
21.  36  sq.  mi.  22.  400  sq.  mi.  23.  900  sq.  ft. 
24.  1600  sq.  ft.  25.  2500  sq.  ft.  26.  3600  sq.ft. 


68  MEASURES 

37.  Illustrative  problems.  1.  If  a  rectangle  has  an  area 
of  15  sq.  in.  and  is  5  in.  long,  how  wide  is  it  ? 

1.  If  a  rectangle  is  5  in.  long  and  1  in.  wide,  area  =  5  sq.  in. 

2.  Therefore  the  number  of  inches  in  width  is  15  sq.  in. 
-f-  5  sq.  in.  =  3.    Therefore  it  is  3  in.  wide. 

Pupils  should  construct  the  figure  by  paper  folding  or  cutting,  or 
should  draw  it,  if  necessary.  Another  form  of  solution  is  given  in 
Ex.  2. 

2.    A  rectangle  32i  in.  long  has  an  area  of  227^  sq.  in. 

What  is  the  width  ?  ,Tr    7 

Work  : 

1.  If  tr  =  the  number  of  inches  in  width,  then  32M227.V 
w  times  32  J  times  1  sq.  in.  =  227^  sq.  in. 

2.  Therefore  zv  =  227i  sq.  in.  -f-  32^  sq.  in.  Z 

3.  Therefore  tv  —  7,  the  number  of  inches  in  width.         65  j  45o 

455 

38.  We  therefore  see  that 

The  member  of  units  of  area  of  a  rectangle,  divided  by  the 
number  of  units  of  length,  equals  the  number  of  units  of  width. 
Or,  briefly,  Area  divided  by  length  equals  width. 

WRITTEN   EXERCISE 

1.  What  is  the  area  of  a  rectangle  5'  x  4'?  Draw  the 
figure  and  explain  all  of  your  work. 

2.  How  wide  is  a  12.95-acre  farm  17  ch.  long?  Consider 
such  farms  as  rectangular. 

3.  How  long  is  a  272-a^re  farm  40  ch.  wide? 

4.  A  room  having  a  floor  area  of  205|  sq.  ft.  is  16  ft.  8  in. 
long.    How  wide  is  it  ? 

5.  A  school  playground  63  ft.  wide  has  an  area  of  4473 
sq.  ft.    How  long  is  it  ? 

6.  How  wide  is  a  295.2-acre  farm  72  ch.  long?  Draw 
to  scale  a  plan  of  the  farm. 


AREAS  59 

7.  What  is  the  area  of  a  rectangle  3.25  in.  by^.75  in.? 

8.  A  rectangle  has  an  area  of  294  sq.  ft.    It  is  17  ft. 
6  in.  long.    How  wide  is  it  ? 

9.  A  floor  has  an  area  of  358|  sq.  ft.    The  room  is  21  ft. 
9  in.  long.    What  is  the  width  ? 

10.  A  floor  has  an  area  of  560  sq.  ft.  The  width  of  the 
room  is  17J  ft.    What  is  the  length? 

11.  Find  the  cost  of  a  farm  120  rd.  by  242  rd.,  at  $75  an 
acre.    Draw  to  scale  a  plan  of  the  farm. 

12.  A  floor  has  an  area  of  288  sq.  ft.  80  sq.  in.  The  room 
is  17  ft.  8  in.  long.    What  is  the  width? 

13.  A  floor  has  an  area  of  788  sq.  ft.  18  sq.  in.  The  room 
is  24  ft.  3  in.  wide.    What  is  the  length? 

_^   14.    A  rectangular  table  top  is  42 J  in.  long,  and  it  has 
an  area  of  1296 J  sq.  in.    What  is  the  width? 

15.  A  page  of  a  book  is  7^  in.  by  4|  in.,  and  the  book 
has  400  pages.    How  many  square  feet  of  page  surface  ? 

16.  A  rectangular  playground  has  an  area  of  188  sq.  yd. 
540  sq.  in.    It  is  14  yd.  9  in.  long.    What  is  the  width? 

^  17.  How  many  square  yards  of  oilcloth  are  needed  for  a 
kitchen  15  ft.  by  21  ft.,  allowing  5%  more  than  the  area 
for  matching  ? 

18.  Two  fields  have  each  a  perimeter  of  376  rd.  One  is 
71  rd.  wide  and  the  other  is  93  rd.  wide.  Find  the  length 
and  area  of  each,  and  draw  a  plan. 

19.  Two  fields  have  each  aji  area  6i  4750  sq.  rd.  One  is 
40  rd.  wide  and  the  other  50  rd.  What  is  the  length  of 
each?  the  perimeter?    Draw  each  to  a  scale. 

^--.20.  A  city  building  lot,  rectangular  in  shape,  is  adver- 
tised as  having  an  area  of  2107  sq.  ft.  The  lot  has  a 
frontage  of  21  ft.  6  in.     What  is  the  depth  of  the  lot? 


60  MEASURES 

JL  Farm  Measures 

WRITTEN   EXERCISE 

/      1.    A  farmer  buys  three  tracts  of  land  of  the  following 
dimensions  :  51  ch.  12  li.  x  20  ch.,  51  ch.  13  li.  x  40  ch., 
52  ch.  X  21  ch.    How  many  acres  in  each  ?  in  all  ? 
51  ch.  12  li.  X  20  ch.  means  51  ch.  12  li.  by  20  ch. 

2.  He  paid  $48.50  an  acre  for  the  land.  What  was  the 
total  cost? 

3.  A  piece  of  the  property  7  ch.  long  and  2  ch.  28  li. 
wide  was  not  tillable.  What  was  the  area  of  this  part?  of 
the  tillable  part?  ' 

4.  The  farmer  grew  wheat  on  a  piece  66f  ch.  long  and 
15  ch.  wide,  and  the  yield  was  13  bu.  to  the  acre.  He  sold  the 
wheat  at  85/  a  bushel.    How  much  did  he  receive  for  it? 

5.  He  grew  oats  on  a  piece  15  ch.  long  and  10  ch.  wide, 
and  the  yield  was  42  bu.  to  the  acre.  He  sold  the  oats  at 
59/  a  bushel.    How  much  did  he  receive  for  it  ? 

6.  He  grew  corn  on  a  piece  20  ch.  long  and  15  ch.  wide, 
and  the  yield  was  34  bu.  to  the  acre.  He  sold  the  corn  at 
56/  a  bushel.    How  much  did  he  receive  for  it? 

7.  He  used  an  acre  for  his  house  and  lawn,  this  piece 
having  a  frontage  of  120  ft.  What  was  the  depth  of  the  lot  ? 
What  was  the  length  of  fence  necessary  to  inclose  it? 

8.  The  house  is  50  ft.  long  and  30  ft.  wide,  and  is  rec- 
tangular in  ground  plan.  How  many  square  feet  are  left 
from  the  acre  ? 

9.  The  farmer  took  for  a  vegetable  garden  a  rectangular 
piece  of  land  60  rd.  in  perimeter,  the  length  being  twice  the 
width.    What  was  the  area  of  the  piece  ? 


PARALLELOGRAMS  61 

ORAL   EXERCISE 

1.    If  we  cut  triangle  T  from  this  parallelogram  and 
place  it  where  X  is,  what  kind  of 
a  figure  have  we?    Try  it.    What     "^^ 
does  this  tell  us  about  the  area  of 
a  parallelogram? 


State  the  areas  of  the  parallelograms  whose  bases  and 
altitudes  are  given  in  JExs,  2-9 : 

2.  160  ft.,  25  ft.  3.    m  ft.,  16f  ft. 

4.  64  in.,  12^  in.  5.    150  ft.,  33^  ft. 

6.  444  in.,  25  in.  7.    303  ft.,  33J  ft. 

8.  800  in.,  125  in.  9.    300  ft.,  66f  ft. 

10.  State  a  rule  for  finding  the  area  of  a  parallelogram. 

39.  Parallelogram.    Illustrative  problem.    What  is  the  area 
of  a  parallelogram  of  base  10  ft.  and  altitude  6  ft.? 

1.  A  rectangle  10  ft.  by  6  ft.  has  an  area  10  times  6  sq.  ft. 

2.  Therefore  the  area  of  the  parallelogram  is  also  60  sq.  ft. 

WRITTEN   EXERCISE 

1.  What  is  the  area  of  a  parallelogram  of  base  16.9  ft. 
and  altitude  7.2  ft.? 

2.  Also  of  base  17  ft.  8  in.  and  altitude  27  in.  ? 

3.  Also  of  base  2  yd.  17  in.  and  altitude  2  ft.  3  in.? 

4.  What  is  the  altitude  of  a  parallelogram  whose  base  is 
129.9  ft.  and  area  303.1  sq.  yd.  ? 

6.    Also  of  one  with  base  26.46  in.  and  area  5.^^  sq.  ft.  ? 

6.  What  is  the  area  of  a  parallelogram  with  a  base 
42.5  ft.  and  altitude  27.8  ft.  ?  with  a  base  6.7  in.  and  alti- 
tude 3.9  in.  ?  with  a  base  345.25  ft.  and  altitude  127.37  ft.  ? 


62 


MEASURES 


ORAL    EXERCISE 

1.  How  do  the  areas  of  these  triangles  compare  with 
the  areas  of  the  rec- 
tangles ?  Then  a  tri- 
angle is  what  part  of  a 
rectangle  of  the  same 
base  and  same  height  ? 

State  the  areas  of  the 
triangles  whose  bases  and  altitudes  are  given  in  Exs,  2-7 : 

2.  80  in.,  75  in.  3.    80  in.,  2h  in. 
4.    16  in.,  125  in.  5.    44  in.,  50  in. 

6.    60  in.,  33J  in.  7.    120  in.,  16f  in. 

8.    State  a  rule  for  finding  the  area  of  a  triangle. 

40.  Triangle.    Illustrative  problem.    What  is  the  area  of  a 
triangle  of  base  18  in.  and  altitude  7  in.  ? 

^  of  18  times  7  sq.  in.  =  63  sq.  in. 


WRITTEN   EXERCISE 

Find  the  areas  of  the  triangles  whose  bases  and  altitudes 
are  given  in  Exs,  1-8 : 

1.  43  ft.,  32  ft.  2.  9.3  ft.,  4.9  ft. 

3.  7.9  in.,  8.7  in.  4.  37i  ft.,  42i-  ft. 

6.  8.7  in.,  6.3  in.  6.  2  yd.  32  in.,  27  in. 

7.  324  in.,  47  in.  8.  3  ft.  4  in.,  2  ft.  8  in. 

9.    A  right-angled  triangle  has  its  three  sides  30  rd., 
40  rd.,  50  rd.    What  is  its  area  in  square  rods  ?  in  acres  ? 

10.    What  is  the  base   of   a  triangle  whose  altitude  is 
6.4  rd.  and  area  \  acre  ?  altitude  7.2  in.  and  area  J  sq.  ft.? 


V 


TRAPEZOIDS  63 

41.  Trapezoid.  A  four-sided  figure  with  two  parallel  sides 
is  called  a  trapezoid. 

42.  Area  of  a  trapezoid.    If  a  trapezoid  T  have  a  duplicate 
. -f ^ f-f. J    cut  from  paper  and  turned 

/  T         \  D  /     over  and  fitted  to  it,  like  Z), 

/ — A i /       the  two  together  make  a 

parallelogram.     (Illustrate  by  paper  cutting.)     Therefore 

The  area  of  a  trapezoid  equals  half  that  of  a  rectangle 
ivith  the  same  altitude  and  with  a  base  equal  to  the  sum  of 
the  two  parallel  sides. 

43.  Illustrative  problem.  What  is  the  area  of  a  trapezoid 
of  altitude  4  in.  and  parallel  sides  8  in.  and  10  in.  ? 

As  above  explained,  the  area  is  ^  of  4  times  (8  +  10)  sq.  in.,  or 
36  sq.  in. 

ORAL    EXERCISE 

State  the  areas  of  the  trapezoids  whose  altitudes  are  first 
given  in  Exs,  1-10^  followed  by  the  two  parallel  sides  : 

1.  6  in.,  7  in.  and  13  in.      2.    8  in.,  3  in.  and  12  in» 

3.  10  in.,  12  in.  and  13  in.      4.    12  in.,  7  in.  and  8  in, 

5.  14  in.,  14  in.  and  16  in.      6.    13  in.,  6  in.  and  14  in. 

7.  22  in.,  21  in.  and  29  in. 

8.  15  in.,  7^  in.  and  12i  in. 

9.  17  in.,  8J  in.  and  llf  in. 

10.  11  in..  Ill  in.  and  18|  in. 

11.  If  the  area  of  a  trapezoid  is  48  sq.  in.,  and  the  par- 
allel sides  are  5  in.  and  7  in.,  what  is  the  altitude  ? 

12.  If  the  area  of  a  trapezoid  is  48  sq.  in.  and  the  alti- 
tude is  6  in.,  what  is  the  sum  of  the  parallel  sides  ?  If  one 
of  these  sides  is  9  in.,  what  is  the  other  ? 


64 


MEASURES 


WRITTEN   EXERCISE 

Find  the  areas  of  the  trapezoids  whose  altitudes  are 
first  given  in  Exs,  1-7^  followed  hy  the  two  parallel  sides: 
1.    5  rd.,  6  rd.  7  ft.  and  9  rd. 
.2.   322  ft.,  427  ft.  and  534  ft. 

3.  127  ft.,  129  ft.  and  148  ft. 

4.  236  in.,  208  in.  and  235  in. 

5.  34  ft.,  27  ft.  8  in.  and  33  ft. 

6.  62  ft.  3  in.,  59  ft.  and  78  ft. 

7.  4  yd.,  2  yd.  27  in.  and  6  yd. 

8.  If  the  area  of  a  trapezoid  is  21  sq.  ft.  16  sq.  in.,  the 
altitude  5  ft.  4  in.,  and  one  of  the  parallel  sides  4  ft.  9  in., 
how  long  is  the  other  parallel  side? 


^<^^. 


Ill 


IV 


75 

/ 

/             75' 

/ 

/vi\ 

Yll 

"^ 
^ 

VIII 

IX 

/ 

/  ^ 

\/i 

/      50'  \ 

^         50' 

loo' 

60'       / 

60' 

Street 

An  irregular  city  block  is  divided  into  lots  as  shawn. 

Find  the  area^  in  square  feet^  of  lots  numbered  as  follows  : 

9.    I.  10.    II.  11.  III.  12.    IV.        13.    V. 

14.    VI.         15.    VII.        16.  VIII.        17.    IX.        18.   X. 


PUBLIC  LANDS 


65 


44.  Laying  out  public  lands.    In  the  more  recently  settled 
parts  of  the  country  land  is  laid  out  as  here  described. 

45.  Principal  meridian.  Through  a  given  tract  a  meridian  is 

chosen  as  the  principal  meridian. 


46.  Base  line.    An  east  and  west 
line  is  chosen  as  the  base  line. 

The  principal  meridian  and  base 
line  are  here  shown. 


mm 


47.  Townships.    Lines    are   run 
parallel  to  the  principal  meridian  and  base  line,  at  intervals 
of  6  mi.    This  divides  the  land  into  townships, 

48.  Ranges.    The  north  and  south  rows  of  townships  are 
called  ranges. 

X  on  the  first  map  is  numbered  T.  2  N.,  R.  3  W. ;  that  is,  the 
second  township  north  of  the  base  line,  in 
the  third  range  west  of  the  meridian. 


W 


6 

5 

4 

3 

2 

1 

7 

8 

9 

10 

11 

12 

18 

17 

IG 

15 

14 

13 

19 

20 

m 

22 

23 

24 

30 

29 

28 

27 

26 

25 

31 

32 

33 

34 

35 

36 

E 


49.  Sections.    A  township  is  divided 
into  sections,  each  1  mi.  square. 

This  map  shows  the  method  of  numbering 
S  these  sections. 

Each  section  is  then  divided  as  shown  in  the  third  map. 

If  this  map  represents  the  shaded  part  Y  of  the  second  map, 
and  that  represents  the  shaded  part  X  of  the 
first  map,  the  shaded  part  here  shown  would  be 
thus  described:  S.W.  \  of  N.W.  i,  Sec.  21, 
T.  2  N.,  R.  3  W.  This  means  the  southwest 
quarter  of  the  northwest  quarter  of  section  21, 
second  township  north,  third  range  west. 

In  sections  of  the  country  where  land  is  not  laid  out  in  this 
way  little  attention  should  be  given  to  this  subject. 


N.W.J 

OF 

N.W. 
i 

N.E.i 
160  A 

P 

8i 

320  A 

66  MEASURES 

WRITTEN   EXERCISE 

Write  the  description,  plot,  and  find  the  area  : 

1.  S.E.  -1,  Sec.  5,  T.  3  S.,  E.  3  W. 

2.  KE.  1,  Sec.  8,  T.  2  N.,  R.  2  W. 

3.  E.  J  of  KW.  i,  Sec.  2,  T.  2  N.,  E.  3  E. 

4.  S.  J  of  S.E.  1,  Sec.  20,  T.  2  S.,  E.  3  W. 

5.  X.  ^  of  S.W.  1,  Sec.  10,  T.  3  S.,  E.  2  E. 

6.  E.  i  of  KW.  1,  Sec.  30,  T.  2  S.,  E.  3  E. 

7.  X.E.  1  of  S.W.  J,  Sec.  5,  T.  1  N.,  E.  1  W^ 

8.  S.W.  4  of  KW.  i,  Sec.  32,  T.  1  S.,  E.  3  E. 

9.  K  W.  I  of  IS^.W.  1,  Sec.  6,  T.  3  K,  E.  3  W. 

10.  How  much  is  this  farm  worth  at  $6o  an  acre: 
W.  1-  of  S.  i  Sec.  3,  T.  2  K,  E.  2  W.? 

11.  How  much  is  this  farm  worth  at  $75  an  acre: 
KE.  1  of  KE.  1,  Sec.  5,  T.  2  S.,  E.  2  E.? 

12.  Find  the  area  of  this  farm  :  S.W.  i,  Sec.  10,  T.  2  S., 
E.  2  E.     Draw  a  plan  of  a  township  and  locate  the  farm. 

13.  Find  the  area  of  this  farm  :  N.  ^,  Sec.  6,  T.  1  X., 
E.  1  E.     Draw  a  plan  of  a  township  and  locate  the  farm. 

14.  Mr.  Simmons  owns  the  S.  i,  KE,  i,  Sec.  3,  T.  2  K, 
E.  3  E.     How  many  rods  of  fence  are  needed  to  inclose  it  ? 

15.  How  far  is  it  from  Mr.  Taylor's  farm,  KW.  i  of 
N.W.  i,  Sec.  16,  T.  1  K,  E.  3  W.,  to  Mr.  Hunt's  farm,  S.W. 
i  of  N.W.  J,  Sec.  28,  T.  1  N.,  E.  3  W.?     Draw  the  map. 

16.  A  road  running  straight  through  a  farm  is  ^  mi.  long 
and  3  rd.  wide.  How  many  acres  in  the  road?  If  hay 
can  be  cut  from  the  sides,  averaging  ^  of  the  area,  and  the 
amount  of  hay  averages  2  tons  to  the  acre  and  is  worth 
$9.50  a  ton,  what  is  gained  by  attending  to  this  crop? 


VOLUMES  67 

II.    MEASURES.     PERCENTAGES.     PROPORTION 
VOLUMES 

ORAL   EXERCISE 

1.  Give  the  table  of  dry  measure. 

2.  Give  the  table  of  cubic  measure. 

3.  Give  the  table  of  liquid  measure. 

4.  A  cellar  is  21'  x  18',  and  9'  deep.     Express  the  dimen- 
sions in  yards ;   the  volume  in  cubic  yards. 

5.  At  50  ct.  a  cubic  yard,  how  much  will  it  cost  to  exca- 
vate a  cellar  containing  126  cu.  yd.  ?    175  cu.  yd.  ? 

21'  X  18'  means  21  ft.  by  18  ft.     6''  x  5''  means  6  in.  by  5  in. 

6.  What  is  the  volume  of  a  box  7"  x  3"  x  8"  ? 

7.  What  is  the  volume  of  a  box  6"  x  5"  x  10"  ? 

8.  How  many  cubic  feet  in  a  room  10'  x  12'  x  9'  ? 

9.  How  many  cubic  feet  in  a  room  12'  x  12'  x  10'? 

Find  the  volumes  of  solids  of  the  following  dimensions: 

10.  3"x4"x7".  11.  2"x8"x9". 

12.  6'x8'xl0'.  13.  5'x9'xll'. 

14.  20'x30'x5'.  15.  3'x8'xll'. 

16.  11"  X  11"  X  10".  17.  6  ft.  X  8  ft.  X  11  ft- 

18.  6  yd.  X  8  yd.  x  2  yd.  19.  4  ft.  x  9  ft.  x  11  ft. 

20.  21  in.  X  20  in.  x  10  in.  21.  5  yd.  x  2  yd.  x  7  yd. 

22.  11  in.  X  12  in.  x  10  in.  23.  2  yd.  x  7  yd.  x  11  yd. 

24.  12  in.  X  12  in.  x  10  in.  25.  3  yd.  x  9  yd.  x  11  yd. 

26.  23  in.  X  20  in.  X  10  in.  27.  5  yd.  x  8  yd.  x  12  yd. 

28.  42  ft.  X  11  ft.  X  10  ft.  29.  5  rd.  x  16  rd.  X  20  rd. 


68  MEASURES 

50.  Illustrative  problem.  What  is  the  volume  of  a  box 
3  ft.  wide,  6 J  ft.  long,  2  ft.  high? 

If  it  were  1  ft.  each  way,  the  volume  would  be  1  cu.  ft. 

But  it  is  3  times  as  wide,  6  J  times  as  long,  and  2  times  as  high. 

Therefore  the  volume  is 

3  times  Q^  times  2  times  1  cu.  ft.,  or  38  cu.  ft. 

If  there  is  any  difficulty  in  understanding  this  fact,  in  this  review, 
inch  cubes  may  be  used  as  in  the  earlier  classes. 

WRITTEN   EXERCISE 

1.  How  many  cords  in  a  pile  of  4-ft.  wood,  5  ft.  high 
and  56  ft.  long?    6  ft.  high  and  128  ft.  long? 

2.  How  many  loads  (cubic  yards)  of  earth  must  be  taken 
out  in  excavating  a  cellar  24'  x  18',  and  7'  deep? 

3.  How  much  will  it  cost  to  excavate  a  ditch  150'  x  2' 
X  6',  at  50/  per  cubic  yard?  at  62^/  per  cubic  yard? 

4.  A  schoolroom  is  32  ft.  8  in.  long,  18 J  ft.  wide,  and 
12j  ft.  high.  What  is  the  number  of  cubic  feet  in  the 
room  ? 

5.  A  tunnel  720  ft.  long  has  a  cross-section  area  of  180 
sq.  ft.  How  much  earth  and  rock  were  excavated  ?  (Imagine 
the  cross  section  10'  x  18'.) 

^^^6.  In  preparing  a  flower  bed  in  a  park  it  was  necessary 
to  fill  in  a  space  60'  x  100'  to  an  average  depth  of  1  J'. 
The  earth  cost  33J/  a  load.  What  was  the  total  cost  of 
the  earth  used  ? 

7.  A  freight  car  is  8'  x  34',  and  the  interior  is  7'  high. 
How  many  cubic  feet  does  it  contain?  If  it  is  filled  with 
grain  to  a  height  of  5',  what  is  the  weight  of  the  grain  at 
60  lb.  to  the  bushel,  allowing  Ij  cu.  ft.  to  the  bushel? 


VOLUMES  69 

8.  A  fish  pond  has  been  excavated  to  a  depth  of  5  ft. 
The  dimensions  of  the  bottom  are  40  ft.  and  30  ft.  How 
much  earth  was  excavated? 

9.  The  size  of  an  ordinary  Nebraska  farm-wagon  box  is 
10  ft.  by  3  ft.,  and  24  in.  to  26  in.  deep.  Find  the  contents 
in  cubic  feet  for  each  of  these  depths  ;  also  in  cubic  inches. 

10.  Such  a  wagon  box  24  in.  deep  contains  50  bu.  of 
shelled  corn.  How  many  bushels  of  shelled  corn  will  such 
a  box  26  in.  deep  contain  ? 

11.  If  a  wagon  box  contains  50  bu.  of  wheat  worth  89/ 
a  bushel,  how  many  loads  must  be  drawn  to  carry  $311.50 
worth?    to  carry  $133.50  worth ? 

^^12.  Prairie  hay  is  heavier  than  eastern  meadow  hay,  a 
cube  of  tTie~^rmeF  7  ft.  on  an  edge  weighing  a  ton  (the 
measurement  taken  30  days  after  the  hay  is  stacked).  If 
it  takes  33^%  more  in  bulk  of  a  certain  eastern  meadow  hay 
to  make  a  ton,  how  many  cubic  feet  to  a  ton  of  the  latter  ? 

13.  What  is  the  weight  of  prairie  hay  that  will  fill  a 
space  30  ft.  long,  17  ft.  6  in.  wide,  and  11  ft.  deep,  taking 
the  number  of  cubic  feet  to  the  ton  suggested  in  Ex.  12? 

14.  What  is  the  weight  of  the  eastern  meadow  hay 
mentioned  in  Ex.  12  required  to  fill  the  space  mentioned 
in  Ex.  13  ? 

15.  A  haystack  is  estimated  to  contain  2600  cu.  ft. 
If  prairie  hay,  what  does  it  weigh,  to  the  nearest  half  ton  ? 
If  eastern  meadow  hay  (Ex.  12)? 

16.  A  schoolroom  is  30  ft.  long,  20  ft.  wide,  and  15  ft. 
high.  If  it  is  occupied  by  29  children  and  the  teacher,  how 
many  cubic  feet  of  air  are  allowed  to  each  ?  If  2400  cu.  ft. 
of  fresh  air  per  hour  should  be  allowed  to  each  person,  how 
many  times  an  hour  should  the  air  be  changed? 


70  MEASURES 

Problems  in  Excavation 

written  exercise 

1.  How  many  cubic  yards  of  earth  must  be  removed  in 
digging  a  tunnel  492  ft.  long,  39  ft.  wide,  and  19  ft.  6  in. 
high? 

2.  If  a  dirt  car  is  27  ft.  long,  6  ft.  wide,  and  3^  ft.  deep, 
how  many  cubic  yards  will  it  carry?  How  many  will  12 
cars  carry? 

3.  If  one  laborer  can  shovel  a  cubic  yard  of  earth  into  a 
car  in  30  min.,  how  long  will  it  take  him  to  load  a  car? 
How  long  will  it  take  15  men?    (See  Ex.  2.) 

4.  How  many  cars  of  the  above  dimensions  will  it  take 
to  remove  the  earth  from  the  tunnel  mentioned  in  Ex.  1  ? 
How  many  trains  of  9  cars  each  ?  Allowing  30  ft.  for  the 
total  length  of  a  car,  how  long  a  train  of  cars  would  be 
needed? 

5.  If  one  laborer  can  remove  the  earth  from  a  space 
20  ft.  long,  6  ft.  wide,  and  6  ft.  deep  in  a  day,  how  long 
will  it  take  100  men  to  remove  the  earth  from  the  tunnel 
above  mentioned? 

6.  If  a  laborer  is  paid  at  the  rate  of  10/  a  load  (cubic 
yard)  of  earth  removed,  what  will  he  earn  in  a  day,  remov- 
ing the  amount  specified  in  Ex.  5  ? 

7.  In  the  first  great  subway  in  New  York  City  9733 
cu.  yd.  of  brick  were  used.  Taking  the  size  of  the  brick 
as  81"  X  4"  X  2",  how  many  bricks  were  used? 

8.  What  will  be  the  earnings  of  a  laborer  who  can 
excavate  a  space  a  yard  wide,  a  yard  deep,  and  12  ft.  long, 
in  solid  rock,  in  one  day,  at  75/  per  cubic  yard?  How 
much  at  87^/  per  cubic  yard  ? 


VOLUMES  71 

ORAL    EXERCISE 

In  Uxs,  1—12^  X  represents  a  missing  number.  What  is 
the  number? 

1.  2  X  6  X  :r  =  24  2.    2  X  3  X  ^  =  42. 

3.  3  X  4  X  ^  =  84.  4.    5  X  6  X  .X  =  90. 

5.  2  X  6  X  ^  =  60.  6.    8  X  8  X  a^  =  64. 

7.  b  X  ^  X  x  =  210.  8.    6  X  9  X  a?  =  108. 

9.  b  X  o  X  x  =  125.  10.    2  X  6  X  ic  =  144. 

11.  X  times  13  cu.  ft.  =  130  cu.  ft. 

12.  X  times  16  cu.  ft.  =  320  cu.  ft. 

13.  If  the  product  of  three  numbers  is  400,  and  two  of 
the  numbers  are  5  and  10,  what  is  the  third  one  ? 

14.  If  the  product  of  three  numbers  is  540,  and  the 
product  of  two  of  them  is  90,  what  is  the  third  number? 

15.  If  a  box  is  9  in.  by  10  in.  by  11  in.,  what  is  its 
cubic  contents  ?  If  the  cubic  contents  of  a  box  9  in.  wide 
and  11  in.  long  is  99  cu.  in.,  how  deep  is  the  box? 

16.  If  a  box  contains  54  cu.  in.,  and  is  9  in.  long  and  3  in. 
wide,  how  deep  is  it? 

17.  If  a  box  contains  24  cu.  in.,  and  the  area  of  the  base 
is  6  sq.  in.,  how  deep  is  the  box  ? 

Griven  the  following  volumes  of  boxes,  and  the  length  and 
breadth,  find  the  depth :    j 

18.  60  cu.  in.,  5  in.,  4  in.  19.  64  cu.  in.,  8  in.,  4  in. 
20.  18  cu.  in.,  3  in.,  2  in.  21.  108  cu.  in.,  9  in.,  6  in. 
22.  63  cu.  in.,  7  in.,  3  in.  23.  160  cu.  in.,  8  in.,  4  in. 
24.  240  cu.  in.,  10  in.,  6  in.  25.  350  cu.  in.,  10  in.,  7  ia 


72  MEASURES 

51.  Illustrative  problems.  1.  How  thick  is  a  block  5  ft. 
long  and  4  ft.  wide,  containing  60  cu.  ft.  ? 

Analysis :  Work : 

If  it  is  X  ft.  thick,  x  times  5  times  4  cu.  ft. 

60  cu.  ft.  ^^     =  3 

^=  60  cu.  ft.  and  x  =  —-. —  =  3.     There-         5x4 

5  times  4  cu.  ft. 

fore  it  is  3  ft.  thick. 

We  may,  if  we  prefer,  give  this  analysis  : 

Since  it  is  5  ft.  long  and  4  ft.  wide,  the  area  of  the  base  is 
20  sq.  ft. 

If  it  were  1  ft.  high,  the  volume  would  be  20  cu.  ft. 

Therefore  it  is  as  many  times  1  ft.  high  as  60  cu.  ft.  -^  20  cu.  ft., 
or  3. 

52.  Hence  we  see  that 

The  number  of  cubic  units  of  volume,  divided  by  the  product 
of  the  numbers  of  units  of  two  dimensions,  equals  the  number 
of  units  of  the  third  dimension. 

This  is  sometimes  less  accurately  expressed  :  The  volume  divided 
by  two  dimensions  equals  the  third  dimension. 

2.  What  is  the  area  of  the  base  of  a  block  2^  in.  high, 
containing  70  cu.  in.  ?  ^5 

If  it  were  1  in.  high,  the  volume  would  be  70  2 

cu.  in.  -^  2^  =  23  cu.  in.     But  the  base  of  such  a     -  ^  "^^  _  no 
block  is  28  sq.  in.  5 

This  might  be  briefly  stated  as  in  §  52  :  The  volume  divided  hy 
the  height  equals  the  area  of  the  base.  This  has  a  meaning  only  as 
we  think  of  the  measures  as  abstract  numbers. 

3.  What  is  the  thickness  of  a  block  containing  100  cu.  in., 
the  base  containing  30  sq.  in.  ? 

If  it  were  1  in.  thick,  it  would  contain  30  cu.  in.  -^  =  3^ 

Therefore    it    is    as    many    times    1    in.    thick    as 
100  cu.  in.  -^  30  cu.  in.  =  3^.      Therefore  it  is  3 J-  in.  thick. 


VOLUMES  73 

WRITTEN   EXERCISE 

1.  How  many  cubic  feet  in  a  hall  80'  x  60'  x  23'  4"  ? 

2.  A  tank  9'  x  16§'  contains  900  cu.  ft.    How  deep  is  it? 

3.  A  box  13"  X  20"  contains  3900  cu.  in.  How  deep  is  it  ? 

4.  A  tank  4'  deep  contains  450  cu.  ft.    What  is  the  area 
of  the  base  ? 

5.  A  hall  22'  high  and  30'  wide  contains  28,600  cu.  ft. 
Find  the  length. 

6.  A  block  containing  700  cu.  ft.  has  a  base  area  of 
56  sq.  ft.    How  thick  is  it? 

7.  A  hall  contains  41,341.3  cu.  ft.    It  is  41.3  ft.  long 
and  36.4  ft.  wide.    How  high  is  it? 

8.  A  box  contains  42.159  cu.  in.    The  area  of  the  bot- 
tom is  10.81  sq.  in.    How  deep  is  the  box? 

9.  A  block  of  granite  is  14  in.  long  and  8.3  in.  wide. 
It  contains  836.64  cu.  in.    How  thick  is  it  ? 

10.  The  floor  of  a  hall  contains  1386  sq.  ft.  The  hall 
contains  15,246  cu.  ft.    Required  the  height. 

11.  A  storeroom  is  14.3  ft.  long,  13  ft.  6  in.  wide,  and 
has  a  capacity  of  2316.6  cu.  ft.    How  high  is  the  room? 

12.  The  floor  of  a  room  is  square  and  contains  144  sq.  ft. 
The  room  contains  1368  cu.  ft.  Eequired  the  three  dimen- 
sions of  the  room. 

13.  A  room  24  ft.  long  and  9  ft.  high,  containing  3240 
cu.  ft.,  is  carpeted  with  plain  ingrain  carpet  1  yd.  wide. 
What  is  the  cost  of  the  carpet  at  75/  a  yard? 

14.  A  room  contains  2110.68  cu.  ft;  The  room  is  16.4  ft. 
long,  and  the  floor  area  is  234.52  sq.  ft.  What  are  the 
three  dimensions  of  the  room  ? 


74  MEASURES 

15.  Express  in  bushels  the  volume  of  a  bin  6  ft.  by  4  ft. 
by  3  ft.  6^  in.,  allowing  2150  cu.  in.  to  the  bushel. 

16.  How  many  bars  of  soap,  each  4  in,  long,  2|  in.  wide, 
and  IJ  in.  thick,  can  be  packed  in  a  box  16  in.  long,  13|  in. 
wide,  and  1  ft.  deep? 

17.  What  is  the  value  of  the  bricks  in  a  kiln  60  ft.  long, 
25  ft.  wide,  and  9  ft.  high,  each  brick  being  8  in.  by  4  in. 
by  2  in.,  at  $9  a  thousand  ? 

18.  The  length  of  a  tank  is  100%  greater  than  its  width, 
and  its  width  is  200  %  of  its  depth.  If  the  width  is  2  yd., 
how  many  gallons  does  it  hold? 

19.  A  cord  of  stone  having  the  same  volume  as  a  cord 
of  wood,  what  is  a  pile  of  stones  27  ft.  long,  5  ft.  wide,  and 
6  ft.  high  worth  at  $4.20  a  cord? 

20.  If  it  takes  550  cu.  ft.  of  clover  hay  to  make  a  ton, 
how  many  tons  will  fill  a  mow  32  ft.  long,  the  width  being 
double  the  depth  and  half  the  length? 

21.  Allowing  231  cu.  in.  to  the  gallon,  how  many  gallons 
in  a  watering  trough  that  is  6  ft.  long  and  16  in.  wide,  the 
ratio  of  its  depth  to  its  width  being  3:4? 

22.  A  bin  21  ft.  6  in.  long  and  10  ft.  wide  is  filled  with 
wheat  to  the  depth  of  5  ft.  Allowing  2150  cu.  in.  to  the 
bushel,  what  is  the  wheat  worth  at  80/  a  bushel  ? 

23.  Find  the  cost  of  the  carpet  needed  for  a  room  11  ft. 
3  in.  wide,  10  ft.  high,  containing  2278  cu.  ft.  216  cu.  in., 
the  carpet  being  27  in.  wide  and  costing  $1.35  a  yard, 
allowing  9  in.  for  matching  on  each  strip  except  the  first. 

24.  A  cellar  is  32  ft.  long,  17  ft.  wide,  and  8  ft.  6  in. 
deep.  How  much  will  it  cost  to  build  the  wall,  1  ft.  thick, 
at  35/  per  cubic  foot,  no  allowance  being  made  for  open- 
ings, and  the  length  of  the  wall  being  determined  by  the 
outside  measure  (thus  doubling  the  corners)  ? 


^V^"" 


LONGITUDE  AND  TIME 


75 


"1      r    I    "^ 

^.I.:^i-_L_tB_ 

-_[__L_L_;._ 
1    1    !    IZ> 

1     1     1     1     1 

— j-h-'r-f- 

"  r  [  "i   i  i   ■ 
A  fir-i^ 

LONGITUDE   AND   TIME 

53.  Axes.    A  point  on  any  surface  may  be  located  by  two 
measures  taken  from  two  inter- 
secting   lines    XX'    (read    ''XX 
prime")  and   YY'.     These  lines 
are  called  axes. 

In  this  figure  the  point  ^  is  2,  1, 
and  the  point  B  is  5,  2. 

Distances  to  the  left  of  YY%  or 
below  XX%  may  be  marked  — . 
Thus,  C  is  -  2,3,  and  2)  is  -1,-2. 

54.  Prime  meridian.  An  arc  on  the  earth's  surface,  from 
the  north  pole  to  the  south  pole,  is  called  a  meridian.  The 
one  through  the  Royal  Observatory  at  Greenwich,  England, 
is  taken  by  most  nations  as  the  prime  meridian. 

55.  Points  on  a  map.  On  a  map  the  lines  taken  for  locat- 
ing points  are  the  equator  and  the  prime  m,eridian. 

56.  Latitude  and  longitude.  Instead  of  giving  the  distances 
from  these  lines  in  miles,  they  are  given  in  degrees.  Thus, 
St.  Louis  is  located  when  we  say  that  it  is  90°  12'  17"  W., 
38°  38'  3.6"  N.  The  distance  in  degrees  east  and  west  from 
the  prime  meridian  is  called  longitude;  north  and  south 
from  the  equator,  latitude. 


WRITTEN   EXERCISE 

1.  Draw  two  axes  and  indicate  the  points  2,  4 ;  7,  6. 

2.  In  the  same  way,  indicate  —  2,  4 ;  —  6,  1 ;  —  5,  5. 

3.  In  the  same  way,  indicate  the  points  —  2,  —  3 ;  —1,-4. 

4.  In  the  same  way,  indicate  the  points  3,  —  2 ;  2,-1 

5.  Draw  a  rough  map,  indicating  a  place  40°  N.,  75°  W. 


76  LONGITUDE  AND  TIME 

57.  Correspondence  of  longitude  to  time.  Since  the  earth 
turns  about  on  its  axis  once  every  24  hours,  the  place  in 
which  we  live  will  pass  through  360°  between  now  and 
this  time  to-morrow.  That  is,  to  the  time  24  hours  will 
correspond  the  longitude  360°.    Therefore 

360°  of  long,  correspond  to  24  hr. 

1°  "      *'    corresponds  ''  jj^of  24  hr.,    or  -^-^  hr.,     or  4  min. 
1'    "      "  "  "    ^V   "    4  min.,  "  j^  "^^n.,   "  4  sec. 

1"  "      ''  "  "    ^V  "    4  sec,    "  jV  sec. 

58.  Apparent  motion  of  the  sun.  Because  the  earth  really 
turns  from  west  to  east,  the  sun  appears  to  pass  from  east 
to  west,  as  trees  seem  to  move  when  we  are  on  the  cars. 

59.  Earlier  west,  later  east.  Because  the  earth  revolves 
360°  in  24  hours,  the  sun  appears  to  pass  through  15°  an 
hour.  Therefore  when  it  is  noon  here  it  is  an  hour  later, 
or  1  P.M.,  15°  east  of  here;  an  hour  earlier,  or  11  a.m.,  15° 
west  of  here;  and  6  hours  earlier,  or  6  a.m.,  90°  west  of  here. 

This  work  belonging  partly  to  geography,  no  illustrations  are  here 
introduced.    The  teacher  should  use  the  globe  as  needed. 

ORAL    EXERCISE 

1.  When  it  is  9  a.m.  here,  what  time  is  it  15°  east  of 
here?  30°  west  of  here?  directly  south  of  here? 

2.  When  it  is  noon  here,  what  time  is  it  30°  east  of  here  ? 
90°  west  of  here  ?  150°  east  of  here?  directly  north  of  here  ? 

3.  What  difference  of  time  corresponds  to  a  difference 
of  longitude  of  7i°?  45°?  60°?  105°?  120°?  165°?  180°? 

4.  Since  1'  of  longitude  corresponds  to  4  sec.  of  time,  to 
what  does  7' correspond?  11'?  15'?  30'?  45'?  60'?  120'? 

5.  Since  1"  of  longitude  corresponds  to  -^^  sec.  of  time, 
to  what  does  30"  correspond?   60"?   45"?   5"?  1"?    150"? 


DIFFERENCE  IN  TIME  77 

60.  Illustrative  problem.  Two  ships  at  sea  are  Qb""  7'  30'' 
of  longitude  apart.     What  is  their  difference  in  time  ? 

1.  Since  1°  corresponds  to  ^  hr.,  65°  correspond  to  65  times 
tV  hr.  =  4J  hr.  =  4  hr.  20  min. 

2.  Since  T  corresponds  to  j^  min.,  7'  correspond  to  7  times 
j\  min.  =  j\  min.  =  28>sec. 

3.  Since  V^  corresponds  to  -^^  sec,  30''  correspond  to  30  times 
j\  sec.  =  2  sec. 

4.  Therefore  the  difference  in  time  is  4  hr.  20  min.  30  sec. 
It  is  apparent  that  the  mere  figures  of  the 

answer   conld    be   obtained   by   this    division,      ^^  )  oo      7^  30 
although  the  reason  would  not  be  so  clear.  4  ^0    oO 

WRITTEN  EXERCISE 

1.  27**  4'  15''  of  longitude  corresponds  to  what  difference 
in  time? 

2.  Two  ships  are  75°  30'  30"  of  longitude  apart.  What 
is  their  difference  in  time  ? 

3.  A  ship  at  62°  3'  40"  W.  receives  a  wireless  telegram 
from  one  at  60°  1'  10"  W.  at  11  a.m.     When  was  it  sent  ? 

4.  For  time  purposes  the  longitude  of  Berlin  is  15°  E., 
and  that  of  Chicago  90°  W.  What  is  the  difference  in 
longitude?  Illustrate  by  a  rough  map.  When  it  is  2  p.m. 
in  Chicago,  what  time  is  it  in  Berlin? 

5.  For  time  purposes  the  longitude  of  San  Francisco  is 
taken  as  120°  W.  When  it  is  noon  in  London  (on  the 
prime  meridian),  what  time  is  it  in  San  Francisco?  When 
it  is  noon  in  San  Francisco,  what  time  is  it  in  London? 

6.  A  steamer  68°  10'  30"  W.  sends  a  wireless  telegram 
to  the  Nantucket  light-ship,  70°  W.,  at  8  :  30  a.m.  At  what 
time  is  it  received  ?  If  transmitted  to  New  York,  75°  W., 
without  loss  of  time,  when  is  it  received  there  ? 


78  LONGITUDE  AND  TIME 

61.  Correspondence  of  time  to  longitude.  Since  24  hours 
correspond  to  360°  of  longitude,  we  have  the  following : 

24  hr.  correspond    to  360°. 
1  hr.  corresponds  to  ^\  of  360°,  or  15°. 
1  min.        "  "  ^V  "     1S°>  "  i°»  or  15'. 

1  sec.  "  "  ^V  "     l^'j   "  ¥y    "  15''- 

62.  Illustrative  problem.  The  difference  in  time  between 
two  ships  is  3  hr.  7  min.  3  sec.  What  is  the  difference  in 
longitude  ? 

1.  Since  1  hr.  corresponds  to  15°,  3  hr.  correspond  to  3  times 
15°  =  45°. 

2.  Since  1  min.  corresponds  to  15',  7  min.  correspond  to  7 
times  15'  =  105'  =  1°  45'. 

3.  Since  1  sec.  corresponds  to  15",  3  sec.  correspond  to  3  times 
51"  =  45". 

4.  Therefore  the  difference  in  longitude  is  46°  45'  45". 

Evidently  the  mere  figures  of  the  answer  could 
be  obtained  by  calling  3  hr.  7  min.  3  sec.  3°  7'  3"        ^°    "^^    3" 

and  multiplying  by  15,  although  the  reason  would  1^ 

not  be  so  clear.  '*^°  ^^  ^^ 

WRITTEN   EXERCISE 

1.  The  difference  of  time  between  two  ships  is  2  hr. 
3  min.  10  sec.    What  is  the  difference  in  longitude  ? 

2.  When  it  is  noon  at  Denver,  it  is  7  p.m.  at  Greenwich. 
What  longitude  does  Denver  use  for  its  time  purposes  ? 

3.  The  difference  in  time  between  the  Harvard  and 
Columbia  observatories  is  8  min.  22.7  sec.  What  is  the 
difference  in  longitude? 

4.  At  10 :  4  A.M.  a  steamer  in  longitude  26°  30'  W.  sends 
a  wireless  message  to  another  steamer.  It  is  received  at 
10  :  19  A.M.    What  is  the  longitude  of  the  second  steamer  ? 


DIFFERE]!^CE  IN  LONGITUDE  79 

5.  When  it  is  noon  in  Greenwich  it  is  9  p.m.  in  Japan. 
What  longitude  does  Japan  use  for  its  time  purposes  ? 

6.  When  it  is  noon  in  Melbourne  it  is  2  a.m.  in  Green- 
wich. What  longitude  does  Melbourne  use  for  its  time 
purposes  ? 

7.  A  traveler  sails  from  New  York  with  his  watch  set 
by  the  time  of  75°  W.  If  the  watch  indicates  2 :  30  p.m. 
when  it  is  5  p.m.  by  the  ship's  time,  in  what  longitude  is  he  ? 

8.  A  traveler  sails  from  England  with  his  watch  set  by 
Greenwich  time.  When  he  reaches  52°  30'  45"  W.,  is  his 
watch  faster  or  slower  than  the  time  of  that  place,  and 
how  much? 

9.  Suppose  a  telegram  sent  from  an  observatory  121° 
32'  48"  W.  at  8  :  40  a.m.  to  another  observatory  73°  8' 
16"  W.,  and  to  require  16  min.  for  transmission.  At  what 
time  will  it  be  received  ? 

10.  Suppose  a  telegram  sent  at  4  p.m.  from  a  place  in 
Germany  15°  E.  to  a  place  in  California  120°  W.  At  what 
time  will  it  reach  its  destination,  allowing  30  min.  for 
repeating  at  various  terminal  offices  ? 

11.  A  ship's  captain  observing  the  sun  finds  that  when 
the  ship  is  on  the  meridian  (that  is,  at  noon)  the  time  is 
3  hr.  7  min.  35  sec.  p.m.  by  a  chronometer  set  by  Green- 
wich time.    What  is  the  ship's  longitude  ? 

12.  Two  observatories  A  and  B  are  connected  by  a  tele- 
graph line.  A  telegram  sent  from  A  at  2  hr.  4  min.  6  sec. 
P.M.  reaches  B  at  4  hr.  8  min.  p.m  The  longitude  of  B  is 
79°  12'  42.2"  W.    What  is  the  longitude  of  A? 

13.  The  officers  of  a  steamer  in  the  Mediterranean  Sea 
find  that  when  the  sun  is  on  the  meridian  the  time  is 
10  o'clock  50  min.  15  sec.  a.m.  by  a  chronometer  set  by 
Greenwich  time.    What  is  the  ship's  longitude? 


80 


LONGITUDE  AND  TIME 


63.  Standard  time.  It  is  so  much  trouble  to  think  of  dif- 
ferences of  time  like  1  hr.  2  min.  17.5  sec,  that  most  civi- 
lized countries  have  adopted  a  system  of  standard  time. 
They  have  considered  all  places  in  one  section  as  having 
the  same  longitude,  some  multiple  of  15°,  so  that  the  dif- 
ferences in  time  from  Greenwich  (the  prime  meridian) 
shall  be  exact  hours,  and  therefore  all  differences  in  time 
shall  also  be  exact  hours. 

For  this  reason  New  York  (73°  oS' 25.5"  W.)  is  considered 
to  have  the  longitude  75°  W.,  and  Chicago  (87°  36'  42"  W.) 
the  longitude  90°  W.  Then  when  it  is  noon  in  England 
(which  is  all  considered  of  longitude  0°)  it  is  5  hours  earlier 
in  New  York,  or  7  a.m.,  and  it  is  6  a.m.  in  Chicago. 

64.  Standard  time  map.  This  map  shows  the  standard 
time  sections  in  the  United   States,  the  irregularities  of 


PACinC  T'VE 


CENTRALTIVE+90^ 


H-!l20° 


the  divisions  being  due  to  the  position  of  railway  termini 
nearly  7^°  from  the  time  meridians. 

When  it  is  noon  in  New  York  it  is  11  a.m.  in  the  Central 
Time  section,  10  a.m.  in  the  Mountain  Time  section,  and 
9  A.M.  in  the  Pacific  Time  section. 


STANDARD  TIME  81 

65.  Standard  time  problems.  Since  for  practical  purposes 
standard  time  is  generally  used,  the  exercises  refer  to  that 
time  unless  the  contrary  is  stated.  The  cities  selected  are 
near  the  time  meridians.  Cities  on  the  line  dividing  two 
time  sections  usually  adopt  one  or  the  other. 

Questions  concerning  the  date  line  and  the  change  of  day  do  not 
involve  arithmetic,  but  belong  rather  to  geography. 

ORAL    EXERCISE 

1.  When  it  is  10  a.m.  in  Iowa,  what  time  is  it  in  New 
York  ?    in  Wisconsin  ?    in  Louisiana  ?    in  Ohio  ? 

2.  What  time  is  it  now  in  your  school  ?  in  Boston?  in 
Florida?    in  Arkansas?  in  Colorado?    in  California? 

3.  When  it  is  10  a.m.  in  San  Francisco,  what  time  is  it 
in  Denver?    in  St.  Louis?    in  Cleveland?    in  Albany? 

4.  When  it  is  9  a.m.  in  Denver,  what  time  is  it  in  Los 
Angeles?    in  New  Orleans ?    in  Cincinnati ?    in  Boston? 

5.  When  it  is  noon  in  California,  what  time  is  it  in 
Illinois?    in  Massachusetts?    (Consult  the  map,  page  80.) 

6.  When  it  is  3  p.m.  in  Milwaukee,  what  time  is  it  in 
Oregon?    in  Louisville ?    in  New  York?    in  Philadelphia? 

7.  When  it  is  1  p.m.  in  New  York,  what  time  is  it  in 
Eichmond?    in  Philadelphia?    in  Chicago?  in  California? 

8.  When  it  is  9 :  30  a.m.  in  New  Orleans,  what  time 
is  it  in  Alabama?  in  Maine  ?  in  Wyoming?  in  San 
Francisco  ?  * 

9.  Suppose  a  telegram  sent  from  New  York  at  1  p.m.  to 
San  Francisco.  If  it  goes  without  loss  of  time,  what  time 
will  it  be  when  it  crosses  the  Mississippi  River?  when  it 
crosses  Colorado?    when  it  reaches  San  Francisco? 


82  LONGITUDE  AND  TIME 

WRITTEN   EXERCISE 

1.  France  uses  the  time  of  Paris  (2°  20'  15"  E.).  When 
it  is  noon,  standard  time,  in  Iowa,  what  is  the  time  in 
France  ? 

2.  Japan  uses  the  time  of  135°  E.  When  it  is  noon  at 
Greenwich,  what  is  the  time  in  Tokyo?  in  St.  Louis?  in 
Portland,  Oregon? 

3.  All  of  Great  Britain  uses  Greenwich  time.  If  it  is 
5  :  30  P.M.  at  Liverpool,  what  is  the  local  time  of  a  ship  in 
17°  16'  30"  W.  longitude  ? 

4.  The  longitude  of  Chicago  is  87°  36'  42"  W.  What 
is  the  difference  between  the  local  (that  is,  the  real  merid- 
ian) and  standard  time? 

5.  Italy  uses  the  Central  European  time  (15°  E.).  When 
it  is  7:30  a.m.  in  Springfield,  Illinois,  what  time  is  it  in 
Rome  (7  hr.  later)  ?    in  London  ? 

6.  When  it  is  1  p.m.  in  London,  what  is  the  time  in 
Paris?    (See  Exs.  1,  3.) 

7.  The  longitude  of  San  Francisco  is  122°  25'  40.8"  W. 
Which  is  the  later,  local  or  standard  time,  and  how- 
much? 

8.  Berlin  uses  the  standard  time  of  15°  E.  The  ton- 
gitude  of  Berlin  is  13°  23'  43.5".  What  is  the  difeerence 
between  the  local  and  standard  time? 

9.  What  is  the  difference  in  standard  and  in  local  time 
between  Berlin  and  San  Francisco?    (See  Exs.  7,  8.) 

10.  At  midnight,  December  31,  75°  time,  the  United 
States  Kaval  Observatory  sends  an  electric  time  signal  to 
various  parts  of  the  world,  indicating  that  a  new  year  is 
beginning  at  Washington.  When  does  the  signal  reach 
California?  Colorado?  Alabama?  England?  Germany? 


STANDARD  AND  LOCAL  TLVIE  83 

66.  Table  of  longitudes,  for  reference : 

Albany         73°  44'  48''  W.  New  York  73°  58'  25|"  W. 

Berlin  13°  23'  43i"  E.  Paris  2°  20'  15"  E. 

Chicago       87°  36'  42"  W.  San  Francisco    122°  25'  40f'  W. 

WRITTEN   EXERCISE 

1.  What  is  the  difference  between  the  local  and  standard 
time  of  New  York  ?  of  Albany  ? 

2.  What  is  the  difference  in  local  time  between  Berlin 
and  Paris  ?  Berlin  and  New  York  ? 

3.  What  is  the  difference  in  local  time  between  Albany 
and  San  Francisco  ?  Albany  and  Paris  ? 

4.  What  is  the  difference  in  local  time  between  New 
York  and  Chicago?   Chicago  and  San  Francisco? 

5.  When  it  is  1  p.m.,  standard  time,  at  Chicago,  what  is 
the  standard  time  at  San  Francisco?  the  local  time? 

6.  When  it  is  noon,  local  time,  at  Albany,  what  is  the 
standard  time  there?  What  is  then  the  standard  time  at 
Chicago? 

What  differences  of  local  time  correspond  to  these  differ- 
ences  of  longitude  ? 

7.  8°  8'  8".  8.  15°  27'  30".  9,  7°  23'  48". 
10.  24°  10'  3".  11.  17°  42'  15".  12.  8°  19'  32". 
13.  2^""  16'  9".  14.  32°  48'  19".  15.  6°  17'  19". 
16.  48°  16'  17".  17.  63°  19'  30".  18.  9°  13'  45". 

What  differences  of  longitude  correspond  to  these  differ- 
ences of  local  time  ? 

19.    3  hr.  4  min.  8  sec.  20.    10  hr.  4  min.  4  sec. 

21.    5  hr.  17  min.  5  sec.  22.    7  hr.  9  min.  18  sec. 

23.    8  hr.  19  min.  7  sec.  24.    5  hr.  50  min.  ^5  sec. 


H 


84 


PERCENTAGE 


PERCENTAGE  REVIEWED 


ORAL   EXERCISE 

1.  F  is  what  part  as  large  as  E  ?  what  per  cent  ? 

2.  E  is  what  part  as  large  as  D  ?  what  per  cent  ? 

3.  F  is  what  part  as  large  as  C  ?  what  per  cent  ? 

4.  F  is  what  part  as  large  as  B  ?  what  per  cent  ? 

5.  F  is  what  part  as  large  as  A  ?  what  per  cent  ? 

Tell  what  per  cent 

6.  E  is  of  C.  7.    E  is  of  D.  8.    D  is  of  C. 
9.    E  is  of  A.          10.    EisofB.           11.    C  is  of  B. 

12.  E  is  of  F.  13.    D  is  of  F.  14.    C  is  of  F. 

E  is  twice  F,  or  f  o  o  of  F,  or  200%  of  F.       . 

15.  A  is  of  D.  16.    C  is  of  E.  17.    D  is  of  E. 

18.  Find  10%,  or  ^^,  of  50,  175,  212,  $327,  $475.50. 

19.  Find  50%,  or  i  of  86.4,  $16.44,  $244.50,  $862.20. 

20.  Find  12i%,  or  J,  of  16,  80,  96,  728,  488,  648,  $840. 

21.  Find  16f  %,  or  i,  of  36,  m,  90,  720,  366,  540,  $636. 

22.  Find  20%,  or  J,  of  75,  90,  250,  305,  555,  750,  $3.50. 

23.  Find  25%,  or  i,  of  64,  96,  324,  4.40,  2.40,  320,  $840. 

24.  Find  33j%,  or  i,  of  63,  96,  3.33,  1.50,  630,  900,  324. 


FINDING  PER  CENTS  85 

Sam  is  6  years  old^  Nora  is  9^  and  Tom  is  12.  Tell 
the  following  'per  cents  : 

25.  Sam's  age  is  what  per  cent  of  Tom's  ? 

26.  Sam's  age  is  what  per  cent  of  Nora's  ? 

27.  Nora  is  what  per  cent  older  than  Sam? 

28.  Sam  is  what  per  cent  younger  than  Nora? 

29.  Nora's  age  is  what  per  cent  of  Tom's?  of  Sam's? 

30.  Tom  is  what  per  cent  older  than  Sam?  than  Nora? 
31:  Nora's  age  is  what  per  cent  of  the  sum  of  Sam's  and 

Tom's? 

32.  Nora's  age  is  what  per  cent  of  the  product  of  Sam's 
and  Tom's? 

33.  Sam's  age  is  what  per  cent  of  the  difference  between 
Nora's  and  Tom's  ? 

It  is  3000  miles  from  London  to  New  York^  1000 
miles  from  New  York  to  Chicago^  and  2000  miles  from 
Chicago  to  San  Francisco,      Tell  the  following  per  cents: 

34.  The  distance  from  Chicago  to  San  Francisco  is  what 
per  cent  of  that  from  London  to  Chicago? 

35.  The  distance  from  New  York  to  Chicago  is  what  per 
cent  of  that  from  London  to  San  Francisco? 

36.  The  distance  from  New  York  to  Chicago  has  what 
ratio  to  that  from  Chicago  to  San  Francisco? 

37.  The  distance  from  New  York  to  San  Francisco  has 
what  ratio  to  that  from  London  to  San  Francisco? 

38.  The  distance  from  London  to  New  York  is  what  per 
cent  greater  than  that  from  New  York  to  Chicago? 

39.  The  distance  from  London  to  New  York  is  what  per 
cent  less  than  that  from  London  to  San  Francisco? 


86  PERCENTAGE 

67.  Terms  used.  When  we  say  that  5%  of  $400  is  $20, 
we  call  5%  the  rate,  $400  the  base,  and  $20  th.Q  per centagey 
terms  already  defined  in  the  earlier  treatment  of  the  subject. 

68.  To  find  any  per  cerit  of  a  number,  multiply  the  number 
by  the  rate. 

That  is,  the  percentage  is  the  product  of  the  base  and  rate. 

69.  The  most  important  per  cents.  The  per  cents  studied 
on  page  84  are  among  the  most  important  of  all,  and  their 
common-fraction  values  must  be  thoroughly  known  before 
taking  up  the  business  arithmetic  on  page  138. 

WRITTEN   EXERCISE 

1.  How  much  is  $448.64  plus  25%  of  itself? 

2.  How  much  is  $369.36  less  33^%  of  itself? 

3.  Express  as  per  cents :  |-,  f ,  y\,  y\,  Z^,  y'v. 

4.  How  much  is  125%  of  $246.80?    of  $1234.40? 

5.  What  is  the  interest  on  $750  for  1  yr.  at  3J%  ? 

6.  How  much  is  93%  of  $623?    of  $275?    of  $350? 

7.  What  is  the  discount  on  $950  worth  of  goods  at  15  %  ? 

8.  If  a  village^  formerly  of  1460  inhabitants  has  gained 
5%  in  population,  what  is  its  population  now? 

Express  as  common  fractions  in  their  simplest  forms  : 

9.  48%.  10.  40%.  11.  85%.  12.  28f%. 
13.  16|%.  14.  22^%.  15.  55|%.  16.  37J%. 
17.  77|%.  18.  27-5-\%.  19.  14f%.  20.  17|%. 
21.    32t%.       22.    27t^o%-       23.    67^%.        24.    53/^% 

Using  common-fraction  equivalents.,  find : 
^    25.    16f%ofl02.  26.    33^%  of  $111.21. 

27.    66§%  of  $729.  28.    12^%  of  $336.48. 


FINDING  PER  CENTS  87 

ORAL   EXERCISE 

1.  Since  125%  =  1^,  find  125%  of  $400. 

2.  Find  150%  of  $200,  $300,  $500,  $1000. 

3.  Find  133J%  of  $300,  $36,  $360,  $450,  $600. 

4.  Find  ir6§%  of  $60,  600  ft.,  360  mi.,  420  lb.,  48  yd. 

5.  Since  75%  =  1  -  i,  find  75%  of  40,  400,  200,  $360. 

6.  Since  66|%  =  1  -  i,  find  662  %  of  30,  66,  45,  $300 

7.  Since  87^%  =  1  -  i,  find  87-^%  of  8,  16,  32,  56,  S8. 

8.  Since  80%  =  1  -  J,  find  80%  of  50,  45,  75,  $5000 

9.  Since  83J%  =  1  -  J,  find  83 J  %  of  600,  60,  66,  $36. 

Find  125  %  of  the  following  : 

10.    44  ft.  11.    50  ft.  12.  $120.  13.  $8.40. 

14.    30  in.  15.    84  yd.  16.  $150.  17.  $1.80. 

18.    $300.  19.    500  ft.  20.  $1000.  21.  $3000. 

Find  150%  of  the  following  : 
22.    66  ft.  23.    82  in.  24.    $150.  25.    $2.40. 

26.    35  in.  27.    45  in.  28.    $250.  29.    $1.10. 

Find  133 1^  %  of  the  following  : 
30.    $330.  31.    $630.  32.    $120.  33.    $2.40. 

34.    $1200.         35.    36  in.  36.    48  ft.  37.    75  rd. 

Find  116|%  of  the  following  : 
38.    $1200.         39.    $660.  40.  2400.  41.    $3.60. 

Find  75  %  of  the  following : 
42.    $440.  43.    $300.  44.    $150.  45.    $220. 

Find  66|  %  of  the  following  : 
46.    $3.30.  47.    $7.50.  48.    $1.20.  49.    $5.40. 


88  PERCENTAGE 

WRITTEN   EXERCISE 

1.  If  20%  of  the  days  of  a  common  year  are  stormy, 
how  many  days  are  not  stormy  ? 

2.  A  dealer  bought  $167.40  worth  of  clocks  and  sold 
them  at  a  profit  of  33^%.    How  much  did  he  gain  ? 

V?        3.    How  much  is  the  interest  on  $642.25  for  1  yr.  at  4%? 
How  much  is  it  for  2  yr. ?    for  J  yr.?    for  2  yr.  6  mo.? 

g  4.  A  village  of  3600  inhabitants  increased  in  population 
15%.  It  then  decreased  5%.  What  was  its  population 
then? 

5.  If  in  a  period  of  72  days  33  J  %  are  cloudy,  and  if  it 
rains  on  16f  %  of  the  cloudy  days,  how  many  of  the  days 
are  rainy? 

6.  A  dealer  bought  $1260  worth  of  goods  and  marked 
them  33 J  %  above  cost.  He  sold  them  at  10%  less  than 
the  marked  price,  at  "  bargain  sales."   What  did  he  make  ? 

7.  A  dealer  bought  $644.80  worth  of  shoes  and  sold 
them  at  a  profit  of  2h^o,  How  much  did  he  gain?  If  he 
failed  to  collect  10%  of  this  gain,  how  much  did  he  really 
make? 

8.  A  dry  goods  dealer  bought  $2460.30  worth  of  Persian 
lawn,  and  marked  it  33  J  %  above  cost.  He  sold  half  of  it, 
and  then  sold  the  rest  at  10%  off  the  marked  price.  How 
much  did  he  gain  ? 

9.  The  number  of  pupils  in  a  school  three  years  ago 
was  235.  The  next  year  there  were  20%  more.  Last  year 
there  were  33  J  %  less  than  two  years  ago.  This  year  there 
are  25%  more  than  last  year.  How  many  are  there  this 
year  ? 


FINDING  THE  RATE  89 


ORAL    EXERCISE 


1.  33 J  is  what  per  cent  of  66f  ?  of  100? 

2.  50  is  what  part  of  lOOJ?  what  per  cent  ? 

3.  $75  is  what  per  cent  of  $150?  of  $37.50? 

4.  1  ft.  equals  what  per  cent  of  1  yd.  ?  of  4  ft.  ? 

5.  40  is  what  per  cent  of  80  ?  of  100 .?  of  60  ?  of  40  ? 

6.  120  is  what  per  cent  of  100  ?  of  60  ?  of  40  ?  of  120  ? 

7.  If  a  quarter  of  the  days  of  last  month  were  rainy, 
what  per  cent  were  not  rainy  ? 

8.  25  is  what  per  cent  of  50  ?  of  75  ?  of  100  ?  of  125  ? 
of  150?  of  200?  of  2500?  of  5000? 

9.  $11  is  what  part  of  $33  ?  what  per  cent?  what  per 
cent  of  $22  ?  of  $55  ?  of  $1100?  of*  $2200? 

The  first  of  these  numbers  is  what  per  cent  of  the  second  P 
10.  50,  40.  11.  60,  20.  12.  75, 15.  13.  90,  60. 
14.  15,20.  15,  21,28.  16.  63,21.*  17.  48,12. 
18.  51,17.  19.  96,24.  20.  11,55.  21.  81,27. 
22.  57,  57.  23.  12,  24.  24.  80, 120.  25.  16,  24. 
26.    75,  37^.     27.    12J,  6^ . '    28.    66f ,  33^.     29.    90, 150. 

The  first  of  these  numbers  is  what  per  cent  greater  than 
the  second?       ^, 

30.    75, 50.       31.    60,40.       32.    44,33.         33.    99,66. 
34.    m,  55.       35.    36,  27.       36.    93,  Q>2.         37.   21, 14. 

The  first  of  these  numbers  is  what  per  cent  less  than  the 
second  ? 

38.    21,  28.  39.    28,  32.  40.    44,  48. 

41.    42,  63.  42.    300,  400.  43.    210,  240. 

44.    52,  104.  45.    108,  120.  46.    150,  200. 


90  PERCENTAGE 

70.  Illustrative  problem.    What  percent  of  $35 is  $11.66f? 
Wo?^k  in  steps :  Actual  work  : 

1.  If  x%  of  $35  =  $11.66|,  OMj 

2.  Thenar%        =  $11.66|  ^  $35         $35)$11.66f 

=  0.33^.  10  5 

3.  Therefore  $11.66|   is   33^%   of  1  16| 

105 


o. 


we  may  simply  note  that  $11|  }}j  _      35      _  1 

-/  of  $35,  which  is  331%.  ^^       3  X  35      3 

35 


71.  The  perceiitage  (part)  divided  hy  the  base  (whole) 
equals  the  rate. 

WRITTEN    EXERCISE 

1.  $82.67  is  what  per  cent  of  $248.01  ? 

2.  $17.42  is  what  per  cent  of  $156.78? 

3.  The  45  pu'pils  in  our  grade  are  what  per  cent  of  the 
225  in  school? 

/.     4.    If  a  man  saves  $187.50  out  of  his  salary  of  $1250, 
what  per  cent  does  he  save  ? 

5.  The  45  minutes  devoted  to  arithmetic  to-day  are  what 
per  cent  of  the  4^  hours  that  we  spend  in  school  ? 

6.  By  how  much  does  the  area  of  Texas,  265,780  sq.  mi., 
exceed  7%  of  that  of  the  United  States,  3,616,484  sq.  mi.  ? 

-^  7.  The  9,789,012  tons  of  sugar  produced  in  the  world 
in  a  certain  year  is  what  per  cent  of  the  10,876,680  tons 
produced  the  following  year? 

8.  The  6.27  inches  of  rainfall  here  last  September  was 
what  per  cent  of  the  total  rainfall  of  41.8  inches  for  the 
year  ending  with  that  month? 


FINDING  THE  RATE  91 

Dressmaking  Problems 

written  exercise 

1.  A  dressmaker  bought  16  yd.  of  velvet  at  $3  a  yard, 
selling  9  yd.  at  a  profit  of  16f  %  and  the  rest  at  a  rate  of 
profit  half  as  great.  What  was  the  rate  of  gain  on  the 
whole  ? 

2.  She  bought  a  25-yd.  box  of  chiffon  velvet  at  $4  a 
yard,  with  10%  off  for  cash,  selling  it  at  $4.35  a  yard. 
What  was  her  gain  per  cent? 

3.  She  bought  a  75-yd.  piece  of  silk  skirt  lining  at  65  ct. 
a  yard.  She  sold  28  yd.  at  90  ct.,  15  yd.  at  95  ct.,  and  the 
remainder,  at  the  close  of  the  season,  at  70  ct.  What  was 
her  per  cent  of  gain  ? 

4.  She 'bought  a  50-yd.  piece  of  silk  waist  lining  at  75  ct. 
a  yard.  She  sold  12  yd.  at  $1  and  10  yd.  at  95  ct.,  but  the 
remainder,  being  kept  in  stock  over  the  season,  had  to  be 
sold  at  65  ct.    What  was  her  per  cent  of  gain  or  loss  ? 

5.  She  bought  a  20-yd.  silk  dress  pattern  at  $2.10  a 
yard,  being  allowed,  as  a  dressmaker,  a  discount  of  5%, 
and  6%  off  for  cash.  She  charged  her  customer  the  marked 
price,  $2.10.    What  was  her  per  cent  of  profit  ? 

6.  She  charged  her  customer  $25.50  for  3  yd.  of  Honiton 
lace,  which  had  cost  her  $7  a  yard.  What  was  her  per 
cent  of  profit? 

7.  She  charged  her  customer  $2  for  findings  for  the 
dress.  These  consisted  of  4  spools  of  silk  at  10  ct.  each, 
1  spool  of  thread  at  5  ct.,  3  yd.  of  featherbone  at  10  ct.,  a 
card  of  hooks  and  eyes  at  8  ct.,  skirt  braid  16  ct.,  plaiting 
30  ct.,  waist  binding  30  ct.,  and  collar  10  ct.  What  was 
her  gain  per  cent  on  the  findings  ? 


92  PERCENTAGE 


Grocery  Problems 


WRITTEN   EXERCISE 


1.  If  a  grocer  pays  15/  a  dozen  for  eggs,  how  many 
must  he  sell  for  25/  to  gain  33  J  %  on  the  cost? 

2.  A  grocer  buys  eggs  at  20/  a  dozen,  and  sells  them  at 
the  rate  of  10  for  25/.    What  is  his  gain  per  cent? 

3.  If  a  man  buys  sugar  at  5/  a  pound,  what  must  he 
charge  for  3^  lb.  in  order  to  gain  20%  on  the  cost? 

4.  A  grocer  buys  sugar  at  $12  per  barrel  of  300  lb.,  and 
sells  it  at  the  rate  of  3  lb.  8  oz.  for  IT/.  What  was  his 
gain  per  cent? 

5.  A  grocer  buys  canned  fruit  at  the  rate  of  17/  a  can 
and  sells  it  at  the  rate  of  $5.10  per  case  of  24  cans. 
What  is  his  gain  per  cent? 

6.  My  butcher's  bill  was  $8  last  week,  my  grocer's  bill 
was  25%  more,  and  my  baker's  bill  was  80%  less  than  my 
grocer's  bill.    What  was  the  total  of  the  three  bills  ? 

7.  My  grocer  offers  me  60  cakes  of  one  kind  of  soap  for 
$3.24,  or  100  cakes  of  another  kind  for  $4.38.  Which  is 
the  more  expensive  per  cake,  and  what  per  cent  more 
expensive  is  it? 

8.  A  grocer  buys  a  crate  of  eggs  containing  40  doz., 
paying  15/  a  dozen.  He  drops  the  crate  and  breaks  5  doz. 
How  many  must  he  sell  for  25/  so  as  still  to  gain  16f  % 
on  the  total  cost? 

9.  A  boy  in  a  grocery  store  receives  $6  a  week.  He 
spends  25%  of  it  for  board,  20%  of  the  remainder  for 
clothes,  and  $1  in  other  ways.  If  he  saves  the  rest,  how 
much  will  he  save  in  a  year  (52  wk.)  ? 


FINDING  THE  BASE  93 


ORAL   EXERCISE 


1.  25  is  ^  of  what  number  ?    50%  of  what  number  ? 

2.  40  is  ^  of  what  number  ?    33  J  %  of  what  number  ? 

3.  Of  what  number  is  50  one  half  ?   one  third  ?    two 
thirds?    10%?    25%?    50%?    100%?    125%?   200%? 

The  following  numbers  are  the  given  per  cents  of  what 
other  numbers  F 

Think  of  the  rate  as  a  common  fraction.  If  7  is  10%  of  a 
number,  it  is  j\  of  the  number.  Hence  the  number  is  70.  If  20 
is  66f%  of  a  number,  it  is  |  of  the  number,  and  J  is  10.  Hence  the 
number  is  30. 

4.  21,  10%.  5.    17,50%.  6.   32,  33J%. 
7.    49,  50%.               8.    63,  33j%.           9.    48,  66f  %. 

10.    150,  75%.  11.    400,  80%.  12.    12,  16f  %. 

13.   100,  8J%.  14.    21,  12^%.  15.   55,  125%. 

16.  330,  150%.  17.  720,  200%.  18.  350,  166f  %. 
19.  99,  1121-%.  20.  81,  112i%.  21.  180,  112^%. 
22.    500,  166§%.       23.    250,  166f %.      24.    276,  110^%. 

25.  If  $6  is  3%  of  a  number,  what  is  1%  of  the  num- 
ber ?     What  is  the  number  ? 

26.  If  $9.12  is  the  interest  on  a  certain  sum  for  1  yr.  at 
3  % ,  what  is  the  sum  ? 

27.  If  $4.50  is  5%  of  a  certain  sura,  what  is  the  sum? 
If  it  is  2J%,  what  is  the  sum  ? 

28.  If  a  piece  of  cloth  shrinks  2  yd.,  the  shrinkage  being 
5%,  what  was  the  original  length? 

29.  A  kettle  of  water  loses  25%  of  its  contents  in  boil- 
ing, and  then  contains  2  qt.  less  than  it  did  at  first.  How 
much  did  it  contain  at  first  ? 


94  PERCENTAGE 

What  is  the  number  which^  if  decreased   by  2b  ^o   of 
itself  becomes  the  following  f 

If  1 50  is  I  of  a  number,  what  is  J  ?  f  ? 

30.    150.        31.    600.  32.    450.  33.    750. 

34.  3750.   35.  2250.    36.  9000.    37.  6300. 

Also^   if  decreased    by    33|^%    of  itself   becomes    the 
folloiving  ? 

38.    240.        39.    400.  40.    500.  41.    600. 

42.    1000.      43.    1200.  44.    1600.  45.    2000^! 

Also^  if  decreased  by  20^o   of  itself  becomes  the  fol- 
lowing ? 

46.    480.        47.    840.  48.    640.  49.    320. 

50.    $80.        51.    $60.  52.    $24.  53.    $36. 

Also^  if  increased  by  16|%   of  itself^  becomes  the  fol- 
lowing ? 

If  140 

54.    140.         55.    350. 

58.    $42.        59.    $70. 

Also^  if  increased  by  12^%   of  itself  becomes  the  fol- 
loiving ? 

62.    |.  63.    90.  64.    63.  65.    81. 

66.    $27.        67.    $18.  68.    $45.  69.    $99. 

Also^  if  increased  by  66|%  of  itself  becomes  the  fol- 
lowing?' 

70.    |.  71.    25.  72.    45.  73.    75. 

74.    $60.        75.    $80.  76.    $100.  77.    $500. 


ist-     t- 

56.   280. 

57.    210. 

60.    $63. 

61.   $49. 

FINDING  THE  BASE  95 

72.  Illustrative  problem.    $13.80  is  6%  of  what  amount? 
Work  in  steps:  Actual  ivork: 

1.  Since  6%  of  a:  =  $13.80,  .06)$13.80 

2.  ^^herefore  x  =  $13.80  -^  0.06,  6 )  \ 


by  dividing  equals  by  6%.  $230 

3.    That  is,  x  =  $230. 

Or  we  may  think  that  since  $13.80  is  6%  of  some  number,  1% 
is  J  of  $13.80,  or  $2.30,  and  100%  is  100  times  $2.30,  or  $230. 

73.    The  percentage  (part)  divided  by  the  rate  equals  the     Ax*^"^ 
base  (whole), 

WRITTEN   EXERCISE 

1.  $9.85  is  2%  of  what  sum?  5%  of  what  sum? 

2.  $1.43  is  4%  of  what  sum?  5%  of  what  sum? 

3.  $1.75^  is  6%  of  what  sum?  10%  of  what  sum? 

4.  $22.68  is  7%  of  what  sum?  20%  of  what  sum? 

5.  On  what  sum  is  $7  the  interest  for  1  yr.  at  4%  ? 

6.  If  $13.50  is  the  interest  on  a  certain  sum  for  2  yr.  at 
3%,  what  is  the  interest  for  1  yr.?  What  is  the  principal? 
^..  7.  A  class  measuring  a  certain  distance  on  a  wall  made 
an  error  of  0.28  ft.,  which  was  0.07%  of  the  total  distance. 
What  was  the  distance? 

.  8.  A  certain  city  has  increased  4230  in  population  in 
ten  years,  which  is  15%  of  the  population  ten  years  ago. 
What  was  the  population  then  ? 

^>-,  9.  A  merchant  gained  $4375  last  year,  which  was  17^% 
of  his  capital.  This  year  he  has  lost  $2750.  What  per 
cent  of  his  capital  has  he  lost  this  year  ? 

10.  A  man  lost  $247.50  in  business  last  year,  or  15%  of 
his  capital  at  the  beginning  of  the  year.  How  much  was 
his  capital  at  the  beginning  of  the  year? 


96  PERCENTAGE 

74.  Illustrative  problems.  1.  A  man  gained  16§%  on  his 
capital  of  $18,000.     How  much  did  he  then  have  ? 

1.  His  capital  +  16f  %  of  his  capital  =  116|%  of  his  capital. 

2.  116|%  of  $18,000  =^21,000,  the  amount  after  the  increase. 

2.  A  village  having  a  population  of  1900  ten  years  ago 
has  since  lost  13%.     What  is  its  present  population? 

1.  Population  —  13%  of  the  population  =  87%  of  the  population. 

2.  87%  of  1900  =  1653,  the  present  population. 

In  the  first  of  these  examples  we  might,  of  course,  find  16f%,  or  |, 
and  add,  and  in  the  second  we  might  find  13%  and  subtract. 

WRITTEN    EXERCISE 

1.  Increase  $2750  by  15%  of  itself;  by  12%  of  itself. 

2.  Decrease  $3500  by  12%  of  itself;  by  8%  of  itself. 

3.  What  is  the  amount  of  $350  and  a  year's  interest  at 
6%  ?  at  5%  ?  at  3i%  ?  at  4^%  ? 

4.  A  school  had  204  pupils  last  year  and  has  16f  %  more 
this  year.     How  many  has  it  now  ? 

5.  What  is  the  amount  of  $825  and  two  years'  interest, 
the  annual  rate  being  4%?  5%?  6%?  4^%? 

6.  A  merchant  starts  the  year  with  $15,500,  and  loses 
'15%  in  his  business.     What  does  he  then  have? 

7.  Decrease  $750  by  50%  of  itself;  that  result  by  50% 
of  itself;  and  that  result  by  50%  of  itself.  The  result  is 
what  per  cent  of  the  $750  ? 

^  8.  A  man  started  in  business  with  $8500.  The  first  year 
he  gained  15%,  and  the  next  year  he  lost  15%  of  what  he 
then  had.     How  much  had  he  then  ? 

9.  Write  out  a  rule  for  finding  the  base  increased  or 
decreased  by  a  certain  per  cent  of  itself,  given  the  base 
and  rate. 


INDUSTRIAL  PROBLEMS  97 

The  Cattle  Industry 
written  exercise 

1.  A  ranchman  owned  960  head  of  cattle  in  the  fall,  but 
the  losses  by  storms  and  disease  brought  the  number  down 
to  928  in  the  spring.    What  was  his  per  cent  of  loss  ? 

2.  In  a  certain  year  cattle  on  the  range  in  the  Southwest 
were  worth  $8.40  a  head  ;  a  few  years  later  they  were  worth 
$13.44  a  head.    What  was  the  rate  of  increase  in  vahie  ? 


%  m^V^?-' '"^'   '^^'^'  '%'^'f>^fi^>"K^'-'  -«^  ""«*  * 


3.  In  another  year  cattle  in  the  same  locality  were  sell- 
ing for  $22.50  a  head,  an  increase  of  80%  in  their  value 
of  five  years  before.    What  was  their  value  then? 

4.  On  the  upland  pastures  in  the  Southwest  it  averages 
about  20  acres  per  head  to  pasture  a  steer  through  the 
winter.    How  many  square  miles  for  1000  head  ? 

5.  A  western  farmer  bought  in  November  of  one  year 
30  steers  at  $48.14  each,  and  fed  them  six  months,  or 
exactly  183  days.  The  corn  cost  him  $9  a  day  for  all  the 
steers,  and  the  hay  10^  a  day  for  each.  He  sold  them  for 
$121.06  each.  How  much  did  he  lose  on  the  lot,  not  con- 
sidering the  interest  on  his  investment  ? 


98 


PERCENTAGE 


Oyster  Industry 


WRITTEN   EXERCISE 

Small  <<seed  oysters"  are  taken  from  natural  beds  off  the  coast. 
They  are  "planted"  in  shallow  water  in  ''beds"  rented  from  the 
state,  and  there  are  fattened.  The  large  ones  are  called  "  box  " 
oysters  ;  the  average  or  small  ones,  "  cullings." 

1.    A  man  gathered  90  bu.  of  box  oysters  and  150  bu.  of 

cullings.    Each  was  what  per  cent  of  the  other?    of  all? 

* 

2.  There  are 

250  box  oysters 
to  a  bushel,  and 
331%  more  cull- 
ings to  a  bushel. 
How  many  box 
oysters  did  the 
man  gather? 
How  many  cull- 
ings ? 

3.  He  sold  the 
box    oysters    for 

$6.75  a  thousand,  which  was  192f  %  as  much  as  he  received 
per  thousand  for  cullings.  How  much,  did  he  receive  for 
all  of  his  cullings? 

4.  He  paid  $^^  rent  for  one  oyster  bed  and  12%  less 
for  another.    What  did  he  pay  for  both  ? 

5.  The  oyster  man  paid  15/  a  bushel  for  shifting  his 
oysters  to  another  bed,  and  ^^%  as  much  for  freight. 
What  was  the  cost  for  both  items  on  250  bu.  ?  He  also  paid 
a  man  $2.50  a  day  for  12  days  for  dredging  (gathering)  and 
culling  (sorting).  What  was  the  total  of  these  three  items 
of  expense? 


/  INTEREST  99 

SIMPLE  INTEREST   REVIEWED 
ORAL    EXERCISE 

Find  the  interest  on  the  following  sums  for  the  times 
and  at  the  rates  specified : 

1.  $2  for  1  yr.  at  5%  ;  at  6%. 

2.  $25  for  lyr.  at  4%;  at  2%. 

3.  $300,  at  5%,  for  1  yr.;  for  2  yr. 

4.  $400,  at  5%,  for  1  yr. ;  for  3  yr. 

5.  $500,  at  6%,  for  1  yr. ;  for  6  mo. 

6.  $700,  at  6%,  for  1  yr. ;  for  IJ  yr. 

7.  $400,  at  6%,  for  2  yr. ;  for  2  yr.  6  mo. 

8.  $250,  at  4%,  for  1  yr.  ;  for  1  yr.  6  mo. 

9.  $1000,  at  5%,  for  3  yr. ;  for  3  yr.  6  mo. 

10.  $2500,  at  4%,  for  1  yr. ;  for  2  yr. ;  for  2-1-  yr. 

11.  $3000,  at  6%,  for  1  yr.  6  mo. ;  for  1  yr.  4  mo. 

12.  $2000,  at  5%,  for  1  yr.  6  mo.  ;  for  2  yr.  6  mo. 

13.  $1500,  at  3%,  for  1  yr. ;  for  2  yr. ;  for  1  yr.  4  mo. 

14.  $5000,  at  6%,  for  1  yr. ;   for  3  yr. ;   for  6  mo.;   for 
3  mo.;  for  1  mo. ;  for  15  da. 

Find    the  amount  of  principal  and  interest   together, 
given  the  following  principals,   rates,  and  times: 

15.  $100,  at  6%,  for  1  yr.;  for  2  yr. 

16.  $300,  at  5%,  for  1  yr. ;  for  2  yr. 

17.  $250,  at  4%,  for  1  yr. ;  for  3  yr. 

18.  $500,  at  4%,  for  1  yr. ;  for  5  yr. 

19.  $1000,  at  4i%,  for  1  yr. ;  for  2  yr. 

20.  $2000,  at  5^%,  for  1  yr.;  for  2  yr. 


100  INTEREST 

75.  Illustrative  problem.  Find  the  interest  on  $500,  at 
6%,  for  2yr.  3  mo.  6  da. 

1.  The  interest  for  one  yr.  is  6%  of  $500,  or  $30. 

2.  For  2  yr.  it  is  2  times  $30  =  $60. 

"    3  mo.,  or  \  yr.,  it  is                     J  of  $30  =      7.50 
"    6  da.,  or  \  of  ^V  l^-,  it  is  i  of  ^2  of  $30  = M 

3.  Therefore  the  total  interest  is  $68.00 

76.  How  to  find  interest.    Therefore,  to  find  interest, 
Find  the  interest  for  one  year,  and  multiply  hy  the  number 

of  years  or  the  part  of  a  year, 

WRITTEN   EXERCISE 

,'  1.    Find  the  interest  on  $275  for  3  yr.  6  mo.  at  5%. 

2.  Find  the  interest  on  $1250  for  7  yr.  11  mo.  at  6%. 

3.  Find  the  interest  on  $630  for  2  yr.  4  mo.  5  da.  at  6%. 

4.  Find  the  interest  on  $345  for  2  yr.  3  mo.  3  da.  at  5%. 

5.  Find  the  interest  on  $290  for  1  yr.  6  mo.  5  da.  at  5%. 

6.  Find  the  interest  on  $350  for  1  yr.  9  mo.  15  da.  at  4  % . 

7.  Find  the  interest  on  $650  for  2  yr.  8  mo.  10  da.  at  6  % . 

8.  Find  the  interest  on  $1575  for  3  yr.  1  mo.  6  da.  at 
5^%;  at  41%;  at  6%. 

9.  A  man  borrowed  $250  on  January  15,  at  6%.  He 
paid  the  principal  and  interest  on  October  15.  How  much 
did  he  pay  ? 

10.  A  man  borrowed  $350  on  January  27,  at  6%.  He 
paid  the  principal  and  interest  on  February  27  of  the  fol- 
lowing year.    How  much  did  he  pay  ? 

11.  A  man  bought  12  head  of  cattle  on  February  1,  at 
/    $45  a  head,  giving  his  promissory  note  at  6%.    He  paid  it 

on  the  16th  of  the  following  April.    What  was  the  amount 
of  principal  and  interest? 


CANCELLATION  101 

77.  Cancellation  used  in  interest.  It  is  often  advisable  to 
shorten  the  work  by  cancellation.  Find  the  interest  on 
$256.75  for  2  yr.  2  mo.  10  da.  at  4^%. 

Since  4J%=f%  =  ^f7,  and  2  yr.  2  mo.  10  da.  =  (730+60  +  10)  da. 
=  800  da.,  we  have 


4  51.35 

^^^  times  9  times  $^^^J^ 

3^^  times  ^j/i^ 
73 


=  -125.32. 


When  the  time  exceeds  1  yr. ,  and  cancellation  is  used,  it  is  better 
to  take  365  da.  to  the  year.  Of  course  this  gives  exact  interest,  as 
described  on  page  108. 

WRITTEN   EXERCISE 

Find  the  interest,  given  the  principal,  time,  and  rate: 

1.  $172.60,  3  yr.  2  mo.  7  da.,  4%. 

2.  $391.75,  3  yr.  8  mo.  17  da.,  4%. 

3.  $235.50,  3  yr.  1  mo.  9  da.,  6%. 

4.  $175.50,  2  yr.  8  mo.  10  da.,  6%. 
.._  6.    $142.80,  1  yr.  3  mo.  15  da.,  5%. 

6.  $273.40,  2  yr.  8  mo.  20  da.,  5%. 

7.  $172.60,  2  yr.  5  mo.  6  da.,  4J%. 

8.  $182.60,  4yr.  8  mo.  17  da.,  5i%. 

9.  $163.40,  3  yr.  9  mo.  15  da.,  5^%. 

10.  $625.50,  2  yr.  11  mo.  25  da.,  5|%. 

11.  $475.50,  3  yr.  10  mo.  15  da.,  4i%. 

12.  $265.50,  2  yr.  10  mo.  20  da.,  4|%. 

13.  $3562.50,  3  yr.  2  mo.  5  da.,  5J%. 


b 


102  INTEREST 

78.  The  Six  Per  Cent  Method.  The  following  short  method, 
known  as  the  Six  Per  Cent  Method,  is  often  convenient. 

Eequired  the  interest  on  $420  for  5  mo.  10  da.  at  6%. 

1.  Since  2  mo.  =  ^  yr.,  the  rate  for  2  mo.  =  ^  of  6%  =  1%. 

2.  Therefore  the  int.  for  2  mo.  =  1%  of  $420  =  $4.20 
and  for                                      2  mo.  more,  4.20 

"      ''                                      1  mo.     '*       I  of  $4.20,          2.10 
"      "  10  da.      "       I  of  $2.10,      JO 

3.  Therefore  the  total  interest  is  $11.20 

Therefore  the  interest  at  6^o  f^^  ^0  days  is  0.01  ofthejjrincl' 
jmlj  for  6  days  0.001  of  the  principal,  and  for  other  periods 
the  interest  can  be  found  from  the  interest  for  these  periods. 

Various  other  forms  of  this  method  are  given,  but  none  is  so 
simple  as  the  above.  This  is  sometimes  spoken  of  as  the  Banker's 
Method.  The  following  method  may  be  taken,  if  desired,  in  which 
case  the  above  should  not  be  taken. 

Since  the  rate  for  1  yr.  is  j§o  of  the  principal, 

1  \ 

and  for  1  mo.  is  —  as  much,  or  -^  of  the  principal, 
12  '100  ^         ^    » 

and  for  1  da.  is  —  of  this,  or  — ^—  of  the  principal,  therefore 
30  '       1000  ^         ^ 

79.  Multiply  the  principal  by  6  times  the  number  of  years 
and  ^  the  number  of  months  as  hundredths,  adding  the  prod- 
uct of  the  principal  by  ^  the  number  of  days  as  thousandths. 

Thus,  to  find  the  interest,  at  6%,  on  $120,  for  2  yr.  3  mo.  9  da. : 
First  method:  Second  method: 

17.20     int.  for  1  yr.  22ii±iof  $120  +  4-of  «120 

7.20  "  "  100                        1000 

1.20  (1%  of  $120)  2  mo.  .27           9     \ 

.60(Vof$1.20)'  1     ^'  =(2r0  +  6-000)^^^^^^^-^^^-^^^- 

^(t%  of  $0.60)  /o    " 

$16.38 


SIX  PER  CENT  METHOD 


103 


80.  Further  uses  of  the  Six  Per  Cent  Method.  After  finding 
the  interest  at  6%,  the  interest  for  other  rates  is  easily- 
found.    Thus,  take  the  interest  at  6%  and 

Subtract  J  of  itself  to  find  the  interest  at  5%, 


a            1    a        a 

a       a         u 

"         "  4%. 

U                 1      il           11 

(       u         a 

"  ii% 

Divide  by  2 

i       a         a 

"  3%  . 

Add  i  of  itself 

i       a         a 

•        "  7%. 

a      1    a        il 

i       il         a            i 

"  8%. 

ORAL 

Find  the  interest  at  6% 

1.  On  $750,  60  da. 

3.  On  $350,  60  da. 

5.  On  $300,  30  da. 

7.  On  $460,  30  da. 

9.  On  $200,  90  da. 

11.  On  $500,  12  da. 

13.  On  $400,  15  da. 

15.  On  $600,  10  da. 

Mnd  the  interest  at  S%  , 

17.  On  $600,  60  da. 
19.  On  $660,  60  da. 
21.    On  $1200,  30  da. 

Find  the  interest  at  4% 
23.    On  $300,  60  da. 
25.    On  $600,  60  da. 
27.    On  $1200,  30  da. 


EXERCISE 


2.  On  $275,  60  da. 

4.  On  $425,  60  da. 

6.  On  $250,  30  da. 

8.  On  $840,  30  da. 

10.  On  $400,  90  da. 

12.  On  $400,  12  da. 

14.  On  $600,  15  da. 

16.  On  $720,  10  da. 

18.  On  $120,  60  da. 

20.  On  $120,  30  da. 

22.  On  $720,  90  da. 


24.  On  $120,  60  da. 
26.  On  $900,  60  da. 
28.    On  $900,  90  da. 


104  INTEREST 

WRITTEN   EXERCISE 

Find  the  interest: 

1.  $320,  8  mo.,  6%.        2.    $240,  7  mo.,  5%. 

3.  $175,  9  mo.,  6%.        4.    $185,  2  yr.  6  mo.,  5%. 

5.  $330,  7  mo.,  8%.        6.    $240,  3  yr.  8  mo.  2  da.,  4%. 

7.  $1200,  2  yr.  6  mo.  3  da.,  3%. 

8.  $475,  2  yr.  2  mo.  2  da.,  4i%. 

9.  $2435,  2  yr.  3  mo.  9  da.,  4%. 

10.  $1765,  3  yr.  2  mo.  5  da.,  4J%. 

11.  $4200,  1  yr.  3  mo.  15  da.,  5%. 

12.  $381.25,  1  yr.  6  mo.  18  da.,  3%. 

13.  $426.40,  1  yr.  6  mo.  20  da.,  5%. 

14.  $692.50,  2  yr.  8  mo.  15  da.,  4^%. 

Find  the  amount  of  principal  and  interest: 

15.  $175,  1  yr.  2  mo.  6  da.,  6%. 

16.  $342,  2  yr.  3  mo.  4  da.,  5%. 

17.  $1725,  2  yr.  8  mo.  6  da.,  4^%. 

18.  $2175,  3  yr.  6  mo.  15  da.,  5%. 

19.  $312.50,  2  yr.  7  mo.  10  da.,  4%. 

20.  $427.25,  1  yr.  8  mo.  3  da.,  5i%. 

21.  $375.50,  2  yr.  6  mo.  4  da.,  ^%. 

22.  $137.50,  1  yr.  7  mo.  2  da.,  4^%. 

23.  $243.75,  3  yr.  2  mo.  8  da.,  2^%. 

24.  A  man  can  buy  $1750  worth  of  goods  on  90  days' 
credit,  or  he  can  get  them  for  $1720  in  cash,  which  he  can 
borrow  for  the  90  days  at  6%.  Which  is  the  better  plan, 
and  how  much  better  is  it  ? 


DIFFERENCE  IN  TIME 


105 


81.  Difference  in  time.    In  working  without  tables,  360 
days  are  usually  considered  a  year,  and  30  days  a  month. 

Thus,  to  find  the  time  from  July  15  to  Octo- 
ber 5  it  is  customary  to  subtract  as  here  shown, 
and  say  that  the  difference  is  2  mo.  20  da.,  or 
80  da.  A  banker,  however,  will  see  by  his 
tables  that  July  15  is  the  196th  day  of  the  year 
and  October  5  is  the  278th  day,  and  that  the 
difference  in  time  is  82  da. 

82.  Table  of  time.    The  following  table  may  be  used : 


10 

mo.  5  da. 

7 

15 

2 

mo.  20  da. 

278 

196 

82 

Jan. 

Feb. 

Mar. 

April 

May 

June 

July 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

January  ,  . 

365 

31 

59 

90 

120 

151 

181 

212 

243 

273 

304 

334 

February 

334 

365 

28 

59 

89 

120 

150 

181 

212 

242 

273 

303 

March  . 

306 

337 

365 

31 

61 

92 

122 

153 

184 

214 

245 

275 

April  . 

275 

306 

334 

365 

30 

61 

91 

122 

153 

183 

214 

244 

May  .  . 

245 

276 

304 

335 

365 

31 

61 

92 

123 

153 

184 

214 

June  . 

214 

245 

273 

304 

334 

365 

30 

61 

92 

122 

153 

183 

July   . 

184 

215 

243 

274 

304 

335 

365 

31 

62 

92 

123 

153 

August 

153 

184 

212 

243 

273 

304 

334 

365 

31 

61 

92 

122 

September 

122 

153 

181 

212 

242 

273 

303 

334 

365 

30 

61 

91 

October 

92 

123 

151 

182 

212 

243 

273 

304 

335 

365 

31 

61 

November 

61 

92 

120 

151 

181 

212 

242 

273 

3{)i 

334 

365 

30 

December 

31 

62 

90 

121 

151 

182 

212 

243 

274 

304 

335 

365 

The  exact  number  of  days  from  any  day  of  any  month  to  the 
corresponding  day  of  any  month  within  a  year  is  found  opposite 
the  first  month  and  under  the  second.  For  example,  from 
November  5  to  May  5  is  181  days ;  to  May  17,  12  days  more. 


WRITTEN    EXERCISE 

Find  from  the  table  the  number  of  days  from: 
1.    July  7  to  November  7.  2.    October  8  to  March  15. 

3.    January  20  to  May  10.         4.    November  25  to  July  7. 
5.    September  7  to  January  7.    6.    August  5  to  December  10. 


106  INTEREST 

Using  the  table  on  page  105  to  find  the  difference  in 
time,  find  the  interest  : 

7.  On  $275,  from  May  2  to  August  17,  at  6%. 

8.  On  $650,  from  July  14  to  October  29,  at  6%. 

9.  On  $675,  from  March  25  to  October  5,  at  5%. 

10.  On  $675.50,  from  March  1  to  July  25,  at  3%. 

11.  On  $645.50,  from  June  2  to  October  19,  at  3%. 

12.  On  $185,  from  February  10  to  August  2,  at  5%. 

13.  On  $725,  from  October  3  to  December  27,  at  6%. 

14.  On  $420.50,  from  May  15  to  November  2,  at  4J%. 

15.  On  $350.75,  from  April  13  to  September  20,  at  4J%. 

Find  the  amount  of  principal  and  interest: 

16.  On  $980,  from  January  7  to  July  2,  at  5%. 

17.  On  $145,  from  March  3  to  January  5,  at  6%. 

18.  On  $75,  from  May  2  to  September  17,  at  6%. 

19.  On  $442.50,  from  May  9  to  January  6,  at  4i%. 

20.  On  $275,  from  August  15  to  February  7,  at  6%.  - 

21.  On  $875,  from  February  12  to  August  5,  at  5%. 

22.  On  $630,  from  September  14  to  March  9,  at  5%. 

23.  On  $675.90,  from  June  6  to  February  1,  at  4i-%. 

24.  On  $825.30,  from  July  15  to  January  20,  at  4^%. 

25.  On  $1027.50,  from  August  9  to  February  2,  at  3%. 

26.  On  $2075.50,  from  September  3  to  January  15,  at  3%. 

27.  What  is  the  interest  on  a  note  for  $275,  dated 
June  17,  and  due  the  following  January  3,  at  5%? 

28.  What  is  the  amount  of  principal  and  interest  on  a 
note  for  $450,  dated  September  21,  and  due  the  following 
August  1,  at  5^%? 


INTEREST  TABLES 


107 


83.  Interest  tables.  Bankers  generally  use  interest  tables 
based  on  360  days  to  the  year,  although  some  use  those  based 
on  365  days,  the  latter  plan  being  the  fairer  but  yielding 
less  interest.    The  following  shows  part  of  an  interest  table. 


3  Months,  6% 

Total 
Days 

1000 

2000 

3000 

4000 

5000 

6000 

7000 

8000 

9000 

Days  over 
3  Mo. 

90 

15.00 

30.00 

45.00 

60.00 

75.00 

90.00 

105.00 

120.00 

135.00 

0 

91 

15.17 

30.33 

45.50 

60.67 

75.83 

91.00 

106.17 

121.33 

136.50 

1 

92 

15.33 

30.67 

46.00 

61.33 

76.67 

92.00 

107.33 

122.67 

138.00 

2 

93    • 

15.50 

31.00 

46.50 

62.00 

77.50 

93.00 

108.50 


124.00 

139.50 

3 

84.  Illustrative  problem.    From  the  table  find  the  interest 
on  $275  for  3  mo.  3  da.  at  6%. 

The  int.  on  $200  is  0.1  that  for  $2000,  or  $3.10 
u  u  u  $70  u  0.01  ''  *'  $7000,  *'  $1.09 
«  ''  <'  $5  ''  0.001  ''  ^*  $5000,  "  $0.08 
<'       '<      "  $275  '<  $4.27 


WRITTEN   EXERCISE 

Find  the  interest  at  6%  in  Exs,  1-6^  using  the  table: 
1.  $2500,  3  mo.  2.  $3450,  92  da. 

3.  $250.75,  91  da.  4.  $5200,  93  da. 

5.  $475.50,  3  mo.  3  da.  6.  $24,300,  3  mo. 

Find  the  interest  at  6Jc^  taking  the  exact  number  of  days 
from  the  table  on  page  105^  and  using  the  above  table : 

7.  $350.75,  December  19  to  March  21. 

8.  $1250,  November  17  to  February  15.    * 

9.  $650,  March  1  to  June  2 ;  May  4  to  August  5. 

10.  $775,  February  9  to  May  13  j  to  May  10 ;  to  May  12. 


108  INTEREST 

85.  Exact  interest.  When  365  days  are  taken  as  a  year, 
and  the  exact  number  of  days  between  the  dates  is  taken, 
the  interest  is  called  exact  interest. 

The  government  and  some  banks  use  exact  interest. 

86.  Illustrative  problem.  What  is  the  exact  interest  on 
$1750  from  July  5  to  September  5  at  5%  ? 

1.  The  exact  difference  in  time  is  62  da.    (See  table,  page  105.) 

2.  The  interest  for  1  yr.  is  5%  of  $1750,  or  $87.50. 

3.  The  interest  for  62  da.  is  3^^  of  $87.50,  or  $14.86. 

WRITTEN   EXERCISE 

1.  Find  the  exact  interest  on  $4800  for  93  da.  at  5%. 

2.  Find  the  amount  of  $525  for  2  yr.  3  mo.  6  da.  at  5%, 
exact  interest;  also  at  6%,  4^%,  3i%. 

3.  Find  the  interest  on  $1260  for  73  da.  at  6%,  360  da. 
to  the  year;  also  the  exact  interest  for  73  da.  at  6%. 

4.  Find  the  exact  interest  on  $450  from  January  3  to 
February  9  at  4%  ;  from  May  17  to  July  20  at  5%. 

5.  What  is  the  difference  between  the  common  interest 
at  360  days  to  the  year,  and  the  exact  interest,  on  $5000 
for  60  days,  at  6%? 

Find  the  exact  interest^  and  also  the  common  interest  at 
360  days  to  the  year^  on  each  of  the  following : 

6.  $420,  6%,  93  da.  7.    $3250,  2%,  192  da. 
8.    $275,  5%,  63  da.  9.    $252.50,  6%,  60  da. 

10.  $450,  5J%,  70  da.  11.    $1250,  4J%,  300  da. 

12.  $3200,  4%,  3  mo.  9  da.      13.    $455.80,  5%,  275  da. 

y  14.  $6000,  4%,  from  April  1  to  June  1. 

15.  $4850,  3%,  from  February  3  to  March  10. 


FINDING  THE  RATE  109 

87.  To  find  the  rate.    Illustrative  problem.    If  the  common 
interest  on  $250  for  3  mo.  6  da.  is  $4,  what  is  the  rate  ? 

1.  The  interest  for  1  da.  is — ,  and  the  interest  for  360  da.  is 
360  times  ^,  or  $15. 

2.  115  is  i^\  of  $250,  and  ^V^  =  0-06. 

3.  Or  we  may  say  that,  since  r%  of  $250  =  $15,  r%  =  $15  -^  $250 
=  0.06. 

That  is, 

88.  The  rate  equals  the  interest  for  one  year  divided  by 
the  principal. 

WRITTEN   EXERCISE 

Given  the  principal^  common  interest^  and  time.,  find 
the  rate : 

1.    $275,  $27.50,  2  yr.  2.    $250.50,  $30.06,  2  yr. 

3.    $420,  $50.40,  3  yr.  4.    $480,  $36,  1  yr.  6  mo. 

5.    $121.25,  $9.70,  2  yr.  6.    $240,  $24,  2  yr.  6  mo. 

7.    $320.50,  $57.69,  3  yr.        8.    $325,  $45.50,  3  yr.  6  mo. 

9.  $275.25,  $55.05,  5  yr.  10.  $240,  $10.50,  1  yr.  3  mo. 
11.  $3500,  $87.50,  10  mo.  12.  $160,  $19.80,  2  yr.  3  mo. 
13.    $220,  $9.35, 1  yr.  5  mo.     14.    $480,  $26.60,  1  yr.  7  mo. 

15.  $31,  $0.93,  1  yr.  6  mo. 

16.  $540,  $60.75,  2  yr.  6  mo. 

17.  $720,  $58.40,  2  yr.  10  da. 

18.  $360,  $22,  1  yr.  6  mo.  10  da. 

19.  $360,  $29.22,  1  yr.  4  mo.  7  da. 

20.  $1240,  $172.05,  2  yr.  9  mo.  9  da. 


110  ^  INTEREST 

89.  To  find  the  time.  Illustrative  problem.  How  long  will 
it  take  the  interest  on  $320  to  amount  to  $28  at  5%  ? 

Since  the  interest  for  1  yr.  is  5%  of  $320,  or  $16,  $28  is  the 
interest  for  f|  of  a  year,  or  1|  yr. 

Or  since  the  interest  for  1  yr.  is  $16,  for  x  years  it  is  $16  x. 
Therefore  $16  a;  =  $28. 

a:  =  $28  ^  $16  =  If. 
Therefore  the  time  is  If  yr.,  or  1  yr.  9  mo. 

90.  The  number  of  years  equals  the  total  interest  divided 
by  the  interest  for  one  year. 

WRITTEN   EXERCISE 

Find  the  time  it  will  take  to  gain  the  common  interest 
stated  in  Exs.  1-10 : 

1.    $240,  $36  int.,  6%.  2.    $280,  $28  int.,  4%. 

3.    $3000,  $155  int.,  2%.       4.    $350,  $17.50  int.,  3%. 

5.    $175,  $12.25  int.,  4%.     6.    $525,  $47.25  int.,  6%. 

7.    $600,  $42.75  int.,  5%.     8.    $230,  $20.70  int.,  4i%. 

9.    $360,  $19.91  int.,  51%.   10.    $2500,  $37.50  int.,  4^%. 
•'     11.    How  long  will  it  take  a  sum  to  double  itself  at  6%  ? 
12.    How  long  will  it  take  $220,  together  with  the  inter- 
est, to  amount  to  $253,  at  6%  ? 

^-  13.  A  girl  had  $250  invested  for  her,  at  6%,  on  her 
birthday.  When  she  became  21  it  amounted,  with  interest, 
to  $400.    How  old  was  she  when  it  was  invested? 

14.  A  father  gave  his  son  his  promissory  note  for  $225, 
due  when  the  son  became  21  years  old.  The  rate  of  interest 
was  5%,  and  when  the  note  became  due  the  principal  and 
interest  together  amounted  to  $303.75.  How  old  was  the 
son  when  the  note  was  given? 


REVIEW  111 

ORAL   EXERCISE 

State  without  explanation  the  interest  on: 

1.  $100,  2  yr.,  6%.  2.  $200,  1  yr.,  6%. 

3.  $400,  1  yr.,  3%.  4.  $200,  2  yr.,  3%. 

5.  $500,  2  mo.,  6%.  6.  $400,  4  mo.,  6%. 

7.  $850,  1  mo.,  6%.  8.  $750,  6  mo.,  6%. 

9.  $640,  3  mo.,  6%.  10.  $880,  3  mo.,  6%. 

11.  $660,  2  mo.,  5%.  12.  $800,  3  mo.,  5%. 

13.  $360,  2  mo.,  4%.  14.  $900,  2  mo.,  4%. 

15.  $500,  4  mo.,  3%.  16.  $650,  4  mo.,  3%. 

17.  $800,  2yr.,  2-^%.  18.  $700,  2  yr.,  2^%. 

The  rate  of  2^%  for  a  year  is  the  same  as  5%  if  the  time  is  2  yr. 
19.    $650,  3  yr.,  3^%.  20.    $975,  3  yr.,  3J%. 

Griven  the  principal,  interest,  and  timeyfind  the  rate: 
21.    $400,  $20,  1  yr.  22.    $500,  $60,  2  yr. 

23.    $600,  $72,  3  yr.  24.    $300,  $36,  4  yr. 

25.    $1000,  $25,  6  mo.  26.    $200,  $6,  9  mo. 

27.    $750,  $7.50,  2  mo.  28.    $640,  $3.20,  1  mo. 

Given  the  interest,  time,  and  rate,  find  the  principal: 
29.    $12,  lyr.,  6%.  30.    $9,  1  yr.,  3%. 

If  ^9  is  3%  of  the  principal,  what  is  1%?     100%? 
31.    $32,  2  yr.,  4%.  32.    $30,  2  yr.,  3%. 

33.    $12,  6  mo.,  4%.  34.    $63,  3  yr.,  3%. 

35.    $4,  1  mo.,  4%.  36.    $10,  2  mo.,  5%. 

Given  the  principal,  interest,  and  rate,  find  the  time  : 
37.    $400,  $20,  5%.  38.    $300,  $36,  6%. 


112  INTEREST 

WRITTEN   EXERCISE 

Find  the  common  interest  in  Exs.  1—^ : 
1.    $3200,  93  da.,  5%.  2/  $2100,  Ij  yr.,  4%. 

3.    $85.50,  6/^  mo.,  6%.        4.    $175,  2yr.4^Vi»Oo  6%. 

Find  the  exact  interest  m  Exs,  5^ : 

'   5.    $3200,  128  da.,  5%.  6.    $5000,  193  da.,  4%. 

7.    $2750,  227  da.,  6%.  8.    $32,460,  230  da.,  5%. 

Given  the  principal  and  common  interest^  find  the  rate : 
9.    $108,  $6,  1  yr.  1  mo.  10  da. 

10.  $36,  $3.66,  2  yr.  6  mo.  15  da. 

11.  $1440,  $77.70,  1  yr.  6  mo.  15  da. 

12.  $2750,  $115.50,  1  yr.  2  mo.  12  da. 

Find  the  time^  given  the  principal^  interest^  and  rate : 

13.  $5500,  $230,  ^%.  14.    $375,  $54.25,  6%. 
15.    $425,  $63.75,  3%.  16.    $2880,  $155.40,  3^%. 

17.  How  long  must  a  man  have  $2750  invested  at 
5%  so  that  the  principal  and  interest  would  amount  to 
$3231.25? 

18.  A  man  borrowed  $8000  in  Boston  at  4^%,  and 
loaned  it  in  Oregon  at  8%.  How  much  did  he  gain  in 
three  years  by  the  transaction  ? 

19.  A  man  has  $250  in  a  savings  bank  at  3%.  He 
leaves  the  principal,  but  draws  out  the  interest  as  it  is 
due.    How  much  does  he  draw  out  in  four  years  ? 

20.  A  man  having  $13,500  invested  at  5%  reinvests 
$4000  of  it  at  5^%,  $5000  of  it  at  3^%,  and  leaves  the 
rest  invested  as  before.  What  is  the  annual  difference  in 
income  ? 


REVIEW  113 

21.  Which  yields  the  better  income,  $1675  at  5%  or 
$1375  at  6%  ?    What  is  the  difference  for  2  yr.  6  mo.  ? 

22.  A  man  receives  $1718.75  interest  in  2  yr.  6  mo.  on 
an  investment  of  $17,500.    What  is  the  rate  of  interest  ? 

23.  A  boy  has  $300  given  to  him  the  day  he  is  14  years 
old.  His  father  invests  it  for  him  in  a  5%  promissory 
note,  due  on  the  day  he  is  21  years  old.  What  is  the 
amount  on  the  day  the  note  is  due? 

24.  A  real  estate  dealer  buys  360  acres  of  farm  land  at 
$30  an  acre,  and  after  keeping  it  7  months  sells  it  at  an 
advance  of  $3.75  an  acre.  The  money  being  worth  to  him 
5%  a  year,  how  much  does  he  gain  by  the  transaction? 

25.  A  man  having  $26,750  invested  in  business  has  found 
that  his  annual  profits  average  18%  a  year.  He  is  offered 
$35,000  for  the  business,  which  he  can  invest  at  4i%.  If 
he  sells  out  and  retires,  what  will  be  his  loss  in  income  ? 

26.  On  April  10  a  coal  dealer  borrowed  $33,250  at  5%, 
with  which  he  purchased  his  summer's  supply  of  coal  at 
$4.75  a  ton.  He  sold  the  coal  at  $5.65  a  ton,  the  buyers 
paying  for  unloading  and  delivery,  and  paid  his  debt  on 
November  16.    How  much  did  he  gain  ? 

27.  I  own  a  house  which  I  rent  at  $25  a  month.  My 
taxes  are  $50  a  year,  my  repairs  $50,  and  my  insurance 
$10.  Would  it  be  better  for  me  to  sell  the  house  for  $5000 
and  invest  the  money  at  4%,  if  my  taxes  would  then  be 
reduced  to  $10?    What  is  the  difference  in  income  ? 

28.  On  October  15  a  dealer  purchased  $1750  worth  of 
goods  for  the  holiday  trade  on  30  days  credit.  At  the  end 
of  that  time  he  gave  his  note  for  2  months  at  6%  a  year. 
He  sold  the  goods  for  $2105,  and  paid  the  note  when 
due.  What  per  cent  did  he  make  on  the  original  purchase 
price  ? 


114       .  REVIEW 

Factory  Problems 
written  exercise 

1.  A  certain  canning  factory  uses  the  product  of  75 
acres  of  peas  during  the  three  weeks'  season.  In  this  time 
it  puts  up  48,000  cans  of  peas.  At  6  days  to  the  week, 
how  many  acres  of  peas  does  it  use  a  day?  How  many 
cans  does  it  put  up  every  3  hours,  allowing  8  hours  to 
the  working  day? 

2.  A  ^-Ib.  stick  of  solder  is  used  to  seal  30  of  these  cans. 
How  many  pounds  of  solder  are  required  for  a  week's  work  ? 
This  solder  being  20%  lead,  how  many  pounds  of  lead  are 
used  in  a  day  ? 

3.  The  steam  kettle  in  which  the  peas  are  cooked  will 
hold  3  baskets,  each  containing  enough  peas  for  250  cans. 
How  many  cans  of  peas  can  be  cooked  in  one  forenoon 
(8  A.M.  to  12  M.)  if  25  min.  are  allowed  to  each  kettleful  ? 

4.  A  farmer  owns  3  of  the  75  acres  mentioned  in  Ex.  1. 
He  therefore  furnishes  the  peas  for  how  many  cans?  If 
he  takes  for  his  pay  50%  of  the  canned  goods  for  which 
he  furnished  the  peas,  how  many  cases  of  24  cans  each 
should  he  receive? 

5.  A  workman  in  the  factory  puts  together  200  of 
these  cases  a  day.  How  long  will  it  take  him  to  put  to- 
gether cases  enough  for  the  season's  output  mentioned  in 
Ex.  1  ?  How  much  will  he  earn  in  that  time,  at  90/  per 
hundred  cases  ? 

6.  The  factory  runs  from  8  a.m.  to  5  p.m.,  with  an  hour 
out  at  noon.  One  day  some  machinery  broke  down,  stop- 
ping all  work  from  10  a.m.  to  2  :  30  p.m.  What  was  the 
total  output  that  day  ? 


THE  GROCERY 


115 


Problems  of  a  Grocer 


WRITTEN   EXERCISE 

1.  Mr.  F.  T.  Barker  has  $20,000  invested  in  his  build- 
ing and  grocery  stock.  Last  year  his  profits  were  $2500. 
What  was  his  rate  of  profit  ? 

2.  Of  the  $20,000  he  owes  $8000,  paying  5^%  interest. 
How  much  did  this  take  from  his  $2500  profit?  What 
rate  of  income  is 
he  receiving  on 
his  own  money? 

3.  Last  sum- 
mer he  bought 
100  muskmelons 
for  $6.50.  He 
sold  half  of  them 
at  9^  each,  33  of 
them  at  the  rate 
of  3  for  25/,  and 
the  rest  he  had 
to  throw  away.    Did  he  gain  or  lose,  and  what  per  cent  ? 

4.  He  bought  300  bananas  for  $4  and  sold  them  at  the 
rate  of  22/  a  dozen.  What  was  his  gain  per  cent?  At  25 f^ 
a  dozen,  what  would  it  have  been? 

5.  He  bought  500  lb.  of  clover  honey  for  $70  and  sold 
all  but  50  lb.  of  it  at  a  profit  of  32%.  The  rest  he  sold  at 
a  loss  of  55%.    Did  he  gain  or  lose,  and  how  much? 

6.  He  employs  4  order  clerks,  paying  them  $12  a  week 
and  J%  commission  on  all  goods  sold.  Their  average  sales 
being  $280,  $220,  $240,  and  $270  a  week  respectively, 
what  is  the  average  weekly  income  of  each? 


!;»rii;si 

I     .'     :"^;ri 

w 

w 

!ins 

-i- 

rap!i 

JSuK'iPffii''  I  m"^ 

m 

'"■' ' ,  •' 

1  \ 

|v,.. 

»««ll^;-  . 

^ 

1 

1  1 

,1  ,.. 

ITmm 

wmL 

,11  -,  ■ 

:it 

|B||l|tt'''.i 

i  lip  Mil  ill  '""" 

1 

i 

1 

Si 

f^ 

116  REVIEW 

7.  He  buys  sugar  at  $20  per  barrel  of  344  lb.,  and  sells 
it  at  6/  a  pound.    How  much  does  he  gain  on  135  lb.  ? 

8.  If  he  can  sell  a  barrel  of  sugar  (see  Ex.  7)  at  the 
rate  of  48/  for  7  lb.,  how  much  will  he  make  on  a  barrel  ? 

9.  If  he  buys  a  45-lb.  chest  of  tea  for  $16.20,  and  sells 
it  at  50/  a  pound,  what  is  his  rate  of  profit  ? 

10.  If  12  chests  of  the  above  tea  were  damaged  by  being 
stored  in  a  damp  place,  and  brought  25/  a  pound,  what 
was  the  loss  ?    What  was  the  per  cent  of  loss  ? 

11.  He  bought  coffee  by  the  100-lb.  bag  at  $20  a  bag. 
At  what  price  per  pound  must  he  sell  this  to  make  45%  ? 

12.  If  he  buys  flour  at  $4.75  a  barrel  and  sells  it  at 
$5.25,  what  profit  does  he  realize  on  51  bbl.  ?  What  is  the 
per  cent  of  profit? 

13.  He  pays  $4  a  box  for  laundry  soap,  100  cakes  to  the 
box,  and  sells  the  soap  at  6  cakes  for  a  quarter.  What  is 
his  gain  on  a  dozen  boxes  ?    his  per  cent  of  gain  ? 

14.  He  bought  15  boxes  of  starch  at  $1.60  a  box.  There 
being  40  lb.  to  the  box,  what  is  his  gain  if  he  sells  it  all  at 
5/  a  pound?    What  is  the  rate  of  gain? 

15.  He  bought  9  cases  of  tomatoes,  2  doz.  cans  to  the 
case,  at  92/  a  dozen.  He  sold  them  at  3  cans  for  a  quarter. 
What  was  his  gain  or  loss  ?    the  per  cent  of  gain  or  loss  ? 

16.  A  box  of  condensed  milk  contains  4  doz.  cans.  If 
he  buys  18  boxes  at  $3.84  each,  and  sells  ^  at  7/  a  can 
and  the  rest  at  a  profit  of  121%,  does  he  gain  or  lose  on  the 
lot,  and  how  much  ? 

•  17.  He  buys  100  5-lb.  caddies  of  Hyson  tea  for  $420 
He  sells  75  caddies  at  a  profit  of  15%,  and  the  rest  at  a 
loss  of  5%.  How  much  did  he  gain?  At  what  price  apiece 
did  he  sell  the  25  caddies  ? 


RATIO  AND  PROPORTION  117 

RATIO  AND  PROPORTION  REVIEWED 

ORAL   EXERCISE 

1.  What  are  the  two  common  ways  of  expressing  the 
ratio  of  3  to  5  ?     Write  them  on  the  blackboard. 

2.  What  must  be  the  nature  of  the  terms  of  a  ratio,  as 
to  similarity?    Illustrate. 

3.  In  the  ratio  4  ft. :  20  ft.,  which  term  is  the  antecedent  ? 
What  is  the  name  of  the  other  term? 

4.  What  does  the  ratio  of  $4  to  $2  equal?  of  4  ft. 
to  2  ft.?  What  is  the  nature  of  the  ratios  of  concrete 
numbers  ? 

State  the  simplest  values  of  the  following  ratios: 


5. 

i- 

6. 

3 

7. 

41- 

8. 

if 

9. 

u- 

0. 

i§- 

11. 

n- 

12. 

U- 

13. 

H- 

14. 

H- 

15.    $5:  $10.  16.    6 in.:  3 in.  17.    10  ft. :  30  ft. 

18.    $6  :  $42.  19.    $68  :  $17.  20.    13  mi. :  104  mi. 

State  the  value  of  ^  in  each  of  the  following : 


21. 

l=- 

22. 

?  =  9. 
5 

23. 

^  =  7. 
4 

24. 

h- 

25. 

^  =  3. 
9 

26. 

|-»- 

27. 

^  =  6. 

7 

28. 

h'- 

29. 

x:3  =  4. 

30. 

a;:  4  =  9. 

31. 

x:  9  =  4. 

32. 

x:S=-6. 

33. 

x:l  =  l. 

34. 

x:8  =  3. 

35. 

x:3  =  ll. 

36. 

0^:9=9. 

37. 

^  =  5. 

38. 

1^  =  2. 

39. 

^=4. 

40. 

^  =  3. 

X 

X 

X 

x 

41. 

^  =  10. 

42. 

'-^  =  3. 

43. 

4-^  =  15. 

44. 

'1  =  5. 

X 

X 

X 

X 

45. 

X      3 
2~6* 

46. 

X      6 
4~8* 

47. 

X       3 
15~5* 

48. 

X  _  3 
20~10* 

118  RATIO  AND  PROPORTION 

91.  Ratio.  The  relation  of  one  quantity  to  another  of  the 
same  kind,  as  expressed  by  division,  is  called  the  ratio  of 
the  first  to  the  second. 

The  ratio  of  $4  to  $6  is  written  —  or  $4  :  $6.    It  equals  |,  or  |. 

92.  Antecedent.    The  first  term  is  called  the  antecedent. 

93.  Consequent.    The  second  term  is  called  the  consequent, 

94.  A  ratio  is  always  abstract,  and  its  tervis  may  he  written 
as  abstract  numbers. 

95.  Illustrative  problems.  1.  If  —  =  2.7,  what  does  x  equal? 

Multiplying  by  3.7,  ^J  x  —  =  3.7  x  2.7, 

or  a:  =  9.99. 

5.44 
2.  Find  the  value  of  x,  given =  1.7. 

Multiplying  by  x,  5.44  =  1.7  a:, 

5.44 
Hence  x  =  — — -  =  3.2. 

1.7 

WRITTEN   EXERCISE 

Find  the  value  of  n  in  each  of  the  foUoiving : 


1. 

f.-- 

2. 

■n.2-'-''- 

3. 

"^     =0.61. 
31.2 

4. 

12.6  =  "-'- 

5. 

^  =  4.2. 
31 

6. 

1.7 

7. 

i.6 

8. 

1^  =  6.3. 
9.3 

9. 

X 

10. 

2-97_^^ 

11. 

^•^^=4.3. 

12. 

45.6      ^  ^ 
==  5.7. 

X 

X 

X 

13. 

X       2.3 
17       4 

14. 

X        4.1 

2.3  ~  1  ' 

15. 

X    _4 
L6~7' 

RATIO  119 

96.  Illustrative  problem.  Eequired  to  separate  $1540  into 
two  parts  having  the  ratio  of  5  to  9. 

Since  6ne  part  contains  $5  when  the  other  contains  $9,  the 
two  will  then  contain  $14. 

Therefore  y^j  belongs  to  the  first  part  and  j\  to  the  second. 
t\  of  $1540  =  $550,  and  j\  of  $1540  =  $990. 
Check.   $550 +  $990  =  $1540. 

97.  Partitive  proportion.  The  separation  of  a  number  into 
parts  having  a  given  ratio  is  called  partitive  projjortion, 

ORAL   EXERCISE 

Separate  into  parts  having  the  ratios  stated  : 
1.    20,  3:7.  2.    20,  2:3.  3.    26,4:9. 

4.    32,  5  :  11.  5.    32,  7:9.  6.   34,  6 :  11. 

7.    18,5:13.  8.    40,7:13.  9.    39,2:11. 

10.    90,13:17.  11.    26,11:2.  12.    24,11:13. 

13.  Two  partners  are  to  divide  $1500  of  profits  in  the 
ratio  of  1  to  2.    What  is  the  share  of  each? 

14.  A  20-ft.  beam  is  to  be  divided  in  the  ratio  of  2  to  3. 
The  point  of  division  is  how  far  from  each  end  ? 

15.  The  ratio  of  cloudy  to  clear  days  in  a  certain  Novem- 
ber was  2  : 3.    How  many  of  the  days  were  clear  ? 

16.  The  ratio  of  cloudy  to  clear  days  in  February,  1904, 
in  a  certain  place,  was  12  :  17.    How  many  days  were  clear? 

17.  In  a  class  of  30,  4  out  of  5  were  promoted.  What 
was  the  ratio  of  promoted  to  nonpromoted  ?  How  many 
failed  of  promotion  ? 

18.  Out  of  44  boys,  some  are  defending  a  fort  and  some 
are  attacking.  The  ratio  of  the  defenders  to  the  others  is 
1  to  3.    How  many  are  attacking  ? 


120  RATIO  AND  PROPORTION 

WRITTEN   EXERCISE 

Separate  into  parts  having  the  ratios  stated : 
1.    528,17:31.         2.    702,13:41.  3.    450,21:29. 

4.    1050,34:41.       5.    13.23,31:32.        6.    15.54,21:53. 

7.  Separate  165  into  3  parts  -having  the  ratio  of  3  to 
5  to  7. 

This  means  that  the  first  is  to  the  second  as  3  to  5,  and  the 
second  to  the  third  as  5  to  7.  That  is,  -f^  of  165  is  the  first,  /^  the 
second,  ^^3^  the  third,  or  |,  \,  j^,  making  33  the  first  part. 

Separate  into  parts  having  the  ratios  stated  : 

8.  273,  5:7:9.  9.    651,  7:11: 13. 
10.    2173,11:13:17.                   11.    33.67,9:11:17. 
12.    4.455,  11 :  21 :  23.                  13.    40.47,  17  :  19  :  21. 

14.  Water  is  composed  of  two  gases,  hydrogen  and 
oxygen,  combined  in  the  proportion  of  2  to  1,  respectively. 
In  390  parts  of  water,  how  many  parts  of  each  gas  ? 

15.  Two  partners  agree  to  divide  their  profits  in  the 
ratio  of  the  amounts  invested  in  the  business.  One  invests 
$4000  and  the  other  $3000,  and  they  make  $2800.  What 
is  the  share  of  each  ? 

16.  Two  farmers  agree  to  pay  for  the  rent  of  a  pasture 
in  the  ratio  of  the  number  of  head  of  cattle  pastured.  One 
pastures  23  head  and  the  other  32,  and  they  pay  $68.75. 
What  is  the  share  of  each? 

17.  Two  men  receive  $25.90  for  picking  apples,  to  be 
divided  in  the  ratio  of  the  number  of  bushels  picked  by 
each.  For  every  66  bu.  picked  by  the  first  the  second 
picked  21  bu.  less.    How  was  the  money  divided  ? 

The  common  expression  "  to  divide  in  the  proportion  of  2  to  3  *' 
means  the  same  as  ''  to  divide  in  the  ratio  of  2  to  3." 


PROPORTION  121 

98.  Proportion.    An  expression  of  the   equality  of   two 
ratios  is  called  a  proportion. 

99.  Illustrative  problems.     1.  In  the  proportion  x  :  17.2 
=  4.3  :  8,  find  the  value  of  x, 

4.3 

^    ^  ^      Multiplying  by  17.2,      _  ;j.^  x  4.3 

17.2        8  '  as  in  §  95,  ^  ~  ^         -  ^"^^^' 

2 

2.  If  21.3  :  17.1  =  3  :  x,  find  the  value  of  x. 

1.  Because  21.3  :  17.1  =  3  :  a:,  we  must  have  17.1 :  21.3  =  x:S. 

2.  That  is,  ^-  =  ^  ,  e^nd  X  ^12^-1  =  2U, 

3      21.3'  ^X'^  ^' 

7.1 


WRITTEN  EXERCISE 

Find  the  value  of  x  : 

1.    0^:18.2  =  9.1:7.3.  2.    a: :  4.1  =  82.7:  82. 

3.    ic:  21.7  =  2.4:  3.3.  4.    a; :  1.37  =  2.4  :  13.7. 

5.    cc  :  3.21  =  4.12  :  6.6.  6.    ic  :  0.32  =  7.21 : 1.8. 

7.    3.17 :  cc  =  4.28  :  3.2.  8.   2.4  :  a;  =  3.8  :  123. 

9.    8.21:  3  =  4.105  :x.  10.    3.9  :4  =a; :  3200. 

,.  11.  A  certain  circle  has  a  circumference  of  182.73  in. 
What  is  the  circumference  of  a  circle  whose  radius  is  to 
that  of  the  first  as  1.7  :  2.91  ? 

12.  A  certain  water  pipe  has  a  diameter  of  1.91  inches. 
What  is  the  diameter  of  a  pipe  whose  circumference  is  to 
that  of  the  first  as  2.6  : 3.42? 

13.  A  certain  fountain  pen  will  write  on  an  average 
4210  words  with  one  filling.  The  amount  of  ink  it  holds  is 
to  that  held  by  a  similar  pen  as  10 :  13.  How  many  words 
will  the  second  pen  average  at  one  filling  ? 


122  RATIO  AND  PROPORTION 

100.  Extremes  and  means.  The  first  and  last  terms  of  a 
proportion  are  called  the  extremes;  the  second  and  third, 
the  means, 

101.  It  is  an  interesting  property  of  proportion,  as  seen 
in  a  case  like  3  _  1 5 

where  3  x  35  =  7  x  15,  that 

<!£he  j^roduct  of  the  means  equals  the  product  of  the  extremes. 

102.  We  also  see  that  if  a; :  21  =  35 :  105, 

21  X  35 

X  = • 

105 

Therefore,  in  any  proportion. 

The  product  of  the  means  divided  hy  the  given  extreme 
equals  the  required  extreme. 

103.  Illustrative  problem.  If  ic:  7  =  13:20,  what  is  the 
value  of  x  ? 

By  §102,  ^=l|i?  =  4H.         . 

WRITTEN  EXERCISE 

1.  A  miller  uses  18  bu.  of  wheat  for  4  bbl.  of  fiour.  How 
many  barrels  can  he  make  from  207  bu.  ? 

2.  He  sells  25  bbl.  of  this  flour  for  $112.50.  At  the 
same  rate,  what  will  he  receive  for  476  bbl.  ? 

3.  The  Bennington  Battle  monument  casts  a  shadow 
125  ft.  10  in.  long  at  the  same  time  that  a  3-ft.  post  casts 
a  15-in.  shadow.    What  is  the  height  of  the  monument  ? 

4.  To  find  the  height  of  a  church  spire  a  boy  meas- 
ured its  shadow,  152  ft.  3  in.,  at  the  same  time  that  a  post 
3  ft.  6  in.  high  was  casting  a  shadow  5  ft.  3  in.  long.  How 
high  was  the  spire  ? 


PROPORTION  123 

5.  How  long  will  it  take  a  train  to  go  148  mi.,  at  the 
rate  of  55^  mi.  in  1  hr.  30  min.  ? 

6.  If  9  men  can  complete  some  work  in  20  hr.,  how 
many  less  men  can  complete  it  in  16  hr.  more  time? 

7.  If  a  man  can  skate  75  yd.  in  8 J  sec,  how  long  would 
it  take  him  to  skate  200  yd.  if  he  could  maintain  this 
rate? 

8.  If  a  man  can  skate  220  yd.  in  19  sec,  how  long 
would  it  take  him  to  skate  5  mi.  if  he  could  maintain  this 
rate? 

9.  If  750  lb.  can  be  transported  100  mi.  for  a  cer- 
tain sum,  how  far  should  J  T.  be  transported  at  the  same 
rate? 

10.  If  6  men  can  complete  some  work  in  15  hr.,  how 
many  men  must  be  added  to  complete  it  in  5  hr.  less 
time? 

11.  If  10  men  can  complete  some  work  in  30  hr.,  how 
many  men  must  be  added  to  complete  it  in  10  hr.  less 
time  ? 

12.  If  a  man  is  rowing  at  the  average  rate  of  1  mi.  in 
6  min.  23y%^3-  sec,  how  long  will  it  take  him  to  row  1  mi. 
550  yd.  ? 

13.  If  a  man  can  swim  45  yd.  in  23  sec,  how  long 
would  it  take  him  to  swim  2  mi.  if  he  could  maintain 
this  rate? 

14.  When  a  sum  of  money  is  divided  among  7  persons 
each  receives  $16.80.  How  much  would  each  receive  if  the 
same  sum  were  divided  among  8  persons? 

15.  One  man  can  do  a  piece  of  work  in  10  da.,  and 
another  in  9  da.  If  the  wages  of  the  first  are  $3.60  a 
day,  what  should  be  the  wages  of  the  second  ? 


124  RATIO  AND  PROPORTION 

104.  Compound  proportion.    An  expression  of  the  equality 

of  the  products  of  ratios  is  called  a  compound  proportion. 

2        5      a:        3 
For  example,  -  of  -  =  -  of  - .   This  may  also  be  written  thus : 
o         7       0        4 


2:3^   _   rx:6 
5:7i~   13:4' 


105.  Inverse  ratio.  The  ratio  2  :  3  is  called  the  inverse  of 
the  ratio  3  :  2. 

Problems  formerly  solved  by  compound  proportion  are  now 
more  frequently  solved  by  analysis  (see  Smith's  Intermediate 
Arithmetic,  p.  169).  Where  it  is  necessary  to  distinguish  the 
ordinary  proportion  of  four  terms  from  compound  proportion, 
the  former  is  called  simple  proportion.  Compound  proportion  may 
be  omitted  without  interfering  with  the  subsequent  work. 


106.  Illustrative  problems.  1.  In  the  compound  proportion 
here  given,  find  the  value  of  x. 

2:31   _    (x:^ 
5:7j  ~   13:4 

1.  Writing  this  in  the  more  familiar  form  of  fractions,  we  have 

2^5      a:         3 
-  of  -  =  -  of  -  • 
3        7      6        4 

2.  If  we  divide  these  equals  by  |,  or  multiply  by  |,  they  will 
still  be  equal.     Therefore 

3.  Since   we   now    have  ^  oi   x,   x   equals  6  times  as  much. 

Therefore 

6  X  I  of  I  of  f  =  a:. 

Therefore  |^  =  x. 

Such  results  should  always  be  checked  by  being  substituted 
for  X  in  the  compound  proportion.  Thus,  f  of  |^  =  |  of  f  J-  of  |, 
for  each  reduces  to  io. 


COMPOUND  PROPORTION  ^        125 

2.  If  4  loads  of  hay  will  last  6  horses  8  weeks,  8  loads 
will  last  how  many  horses  3  weeks  ? 

1.  Considering  only  the  number  of  loads  in  relation  to  the 
number  of  horses,  the  ratio  of  the  latter  equals  the  ratio  of  the 
former,  for  twice  as  many  horses  will  need  twice  as  many  loads, 
and  so  on.    Therefore 

X  horses  :  6  horses  =  8  loads  :  4  loads,  or  a; :  6  =  8  : 4. 

2.  Considering  only  the  number  of  weeks  in  relation  to  the 
number  of  horses,  the  ratio  of  the  latter  equals  just  the  inverse 
ratio  of  the  former ;  for  if  we  have  twice  as  many  horses,  the  hay 
will  last  only  half  as  long,  the  number  of  weeks  diminishing  in 
the  same  ratio  that  the  number  of  horses  increases.    Therefore 

X  horses  :  6  horses  =:  8  weeks  :  3  weeks,  or  a; :  6  =  8  :  3. 

3.  Finally,  considering  both  the  loads  and  the  time,  we  have 

"^'-|8:3' 
or,  in  the  more  familiar  form  of  fractions, 

2 

a:88  ^^i.8„^ 

-  =  -  of  - ,       whence  a;  =  ^  x  -^  of  15  =  32, 
6      4        3'  "^      i        ^ 

the  number  of  horses. 

107.  We  may  simplify  the  actual  work  by  noticing  that, 
as  in  simple  proportion, 

In  any  proportion  the  product  of  the  means  equals  the 
product  of  the  extremes. 

Hence,  in  the  above  example,  after  reasoning  out  the  form  of 
the  proportion,  we  have  simply  to  write 

4x3x:r=i:6x8x8. 

2      2 

^^^211^=32. 
^x^ 


126  RATIO  AND  PROPORTION 

WRITTEN   EXERCISE 

1.  If  4  bbl.  of  flour  last  6  persons  12  mo.,  how  many 
barrels  will  last  15  persons  18  mo.  ? 

2.  If  75  hens  eat  16  bu.  of  feed  in  12  wk.,  how  many 
bushels  will  30  hens  eat  in  5  wk.? 

3.  If  a  farm  130  rd.  by  80  rd.  costs  $1750,  how  much 
will  one  118  rd.  by  50  rd.  cost  at  the  same  rate  ? 

4.  If  the  total  cost  of  feeding  75  hens  for  7  wk.  is 
$10.50,  what  will  it  cost  to  feed  40  hens  for  9  wk.? 

5.  If  4  five-cent  loaves  of  bread  last  6  persons  2  da., 
how  many  ten-cent  loaves  will  last  5  persons  a  week  ? 

6.  If  $800  yields  $324  interest  in  6  yr.  9  mo.,  how 
much  interest  will  $500  yield  in  4  yr.  5  mo.  at  the  same 
rate  ? 

7.  In  a  sewing  guild  18  girls  make  40  garments  in 
4  hr.  At  this  rate,  how  many  garments  can  30  girls 
make  in  3  hr.? 

8.  If  the  value  of  the  eggs  laid  by  75  hens  in  12  wk. 
is  $67.50,  what  is  the  value  of  the  eggs  laid  by  a  third  as 
many  hens  in  5  wk.  ? 

9.  If  5  boys,  working  8  hr.  a  day,  can  build  a  cabin  in 
the  woods  in  12  da.,  how  many  days  will  it  take  15  boys 
working  2  hr.  less  a  day  ? 

10.  If  5  girls  in  a  sewing  class  make  20  aprons  in  3  da., 
how  many  girls  will  it  take  to  make  32  aprons  in  4  da.? 
to  make  16  aprons  in  6  da.  ? 

11.  A  stone  wall  is  to  be  constructed  around  a  rectan- 
gular piece  of  land  2000  ft.  by  1075  ft.  Ten  men,  working 
8  hr.  a  day,  build  890  ft.  in  3  da.  The  number  of  men  is 
then  diminished  50%,  and  the  remainder  work  9  hr.  a  day. 
How  long  will  it  take  to  complete  the  wall? 


COMPOUND  PROPORTION  127 

)  12.  If  25  children  use  10  boxes  of  crayons,  200  in  a 
box,  in  4  mo.,  how  long  will  6  boxes,  100  in  a  box,  last  40 
children  ? 

13.  If  2  pumps,  working  10  hr.  a  day  for  4  da.,  can  raise 
120  T.  of  water,  how  many  tons  can  3  pumps  raise  in  5  da. 
of  8  hr.  each? 

14.  If  5  men,  working  14  da.,  6  hr.  a  day,  can  excavate 
a  cellar,  how  long  will  it  take  if  there  are  7  more  men,  and 
they  work  1  hr.  longer  each  day  ? 

15.  If  it  will  take  5  boys  14  da.,  working  6  hr.  a  day, 
to  clear  a  stony  field  for  a  ball  ground,  how  long  will  it 
take  12  boys,  working  8  hr.  a  day? 

16.  Two  men  rented  a  pasture  for  $83.  The  first  puts 
in  6  horses  for  4  mo.,  the  second  puts  in  5  horses  for  3^  mo. 
What  is  the  share  to  be  paid  by  each? 

17.  If  it  takes  6  boys  15  da.,  working  4  hr.  a  day,  to 
build  a  playhouse,  how  many  boys  should  be  able  to  do 
the  work  in  12  da.,  working  3  hr.  a  day? 

18.  If  9  girls  in  a  manual  training  class  made  12  baskets 
in  4  da.,  working  45  min.  a  day,  how  many  baskets  can 
15  girls  make  in  6  da.,  working  an  hour  a  day  ? 

19.  If  a  railroad  charges  $9  for  transporting  3  T.  of 
goods  360  mi.,  how  much  should  be  charged  for  transport- 
ing 1\  T.  of  goods  280  mi.  at  the  same  rate? 

20.  If  5  girls,  earning  money  for  Christmas  gifts, 
dressed  14  dolls  in  4  da.,  working  6  hr.  a  day,  how  many 
dolls  could  8  girls  dress  in  3  da.  of  5  hr.  each,  at  the  same 
rate? 

21.  Of  2  boys  raising  eggs  for  the  market,  one  has  40 
hens  and  the  other  75.  If  the  40  hens  lay  1440  eggs  in 
12  wk.,  how  many  will  the  75  hens  lay  in  half  that  time, 
at  the  same  rate  ? 


128  REVIEW 

Farm  Problems 
written  exercise 

Estimate  the  answers,  putting  the  estimates  in  writing  for  comr 
parison  with  the  correct  answers.    Some  estimates  should  be  exact. 

1.  A  meadow  is  19  J  rd.  long  and  9  J  rd.  wide.  What  is 
its  area  in  acres  ? 

2.  A  square  bin  has  a  capacity  of  2352  cu.  ft.  The  bin  is 
51  ft.  deep.  What  is  its  length  ?  (Given  that  441  =  21  x  21.) 

3.  If  1  qt.  of  corn  will  plant  230  hills,  what  will  the 
corn  cost  for  2760  hills  @  25/  a  quart  ? 

4.  If  1  qt.  of  beans  will  plant  150  hills,  what  will  the 
beans  cost  for  1950  hills  @  35/  a  quart  ? 

5.  What  is  the  cost  of  seed  for  7500  celery  plants, 
allowing  ^  oz.  to  1000  plants,  @  22/  an  ounce? 

^    6.    What  is  the  cost  of  seed  for  3500  cauliflower  plants, 
allowing  1  oz.  to  1000  plants,  @  $2.30  an  ounce  ? 

7.  Find  the  cost  of  oats  required  to  sow  15  acres,  allow- 
ing 2i  bu.  to  the  acre,  the  oats  being  worth  90/  a  bushel. 

8.  Find  the  cost  of  beans  required  to  plant  5  acres, 
allowing  12  qt.  to  the  acre,  the  beans  being  worth  $1.50  a 
peck. 

^  9.  Find  the  cost  of  peas  required  to  plant  5  acres, 
allowing  1 J  bu.  to  the  acre,  the  peas  being^  worth  $3.50  a 
bushel. 

10.  Find  the  cost  of  corn  required  to  plant  20  acres, 
allowing  8  qt.  to  the  acre,  the  corn  being  worth  $2  a 
bushel. 

11.  Find  the  cost  of  potatoes  required  to  plant  12  acres, 
allowing  10  bu.  to  the  acre,  the  potatoes  being  worth 
$1.15  a  bushel. 


FARM  PROBLEMS 


129 


12.  If  a  tree  sparrow  eats  an  ounce  of  weed  seed  every 
4  days,  how  many  pounds  will  500  such  birds  eat  in  May? 

13.  If  a  tree  sparrow  eats  in  a  day  enough  seeds  to 
produce  75  weeds,  a  dozen  such  birds  will  destroy  in  a 
week  enough  seeds  to  produce  how  many  weeds? 

14.  If  a  woodpecker  eats  on  an  average  1690  insect 
pests  in  a  day,  how  many  will  250  wood- 
peckers eat  during  June  ? 

^  15.  If  a  woodpecker  eats  on  an  average 
10%  less  insect  pests  in  May  than  in  June, 
how  many  will  50  woodpeckers  eat  during 
May?    (See  Ex.  14.) 

16.  The  king  bird  eats  89%  animal  food. 
Out  of  11  lb.  8  oz.  of  food  eaten  by  these 
birds,  how  many  ounces  are  vegetable  food  ? 

17.  Of  the  food  of  bobolinks,  63%  is 
insects.  How  much  insect  food  is  con- 
sumed by  them  while  eating  7  lb.  6f  oz.  of 
other  (vegetable)  food? 

18.  Of  the  food  of  blackbirds,  57%  is  weed  seed.  When 
these  birds  have  consumed  14J  lb.  of  other  food,  how  many 
pounds  of  weed  seed  have  they  eaten? 

y  19.  Out  of  5  lb.  of  food  eaten  by  orioles,  12|  oz.  consist 
of  vegetable  food,  the  remainder  being  insects  injurious  to 
plant  life.  What  per  cent  of  the  food  is  injurious  to  plants  ? 

20.  It  is  estimated  that  the  offspring  of  a  pair  of  English 
sparrows  would,  were  there  no  deaths,  amount  in  ten  years 
to  275  million.  Estimating  75%  of  the  food  of  these  birds 
to  be  grain,  and  allowing  \  oz.  of  food  to  each  bird  daily, 
how  many  pounds  of  grain  would  this  offspring  consume  in 
a  day  ?  in  365  da.  ? 


130  REVIEW 

21.  If  a  heaped  barrel  of  potatoes  contains  3  bu.,  how 
many  such  barrels  will  contain  567  bu.  ?  How  many  bushels 
in  297  such  barrels  ? 

22.  The  2,568,391,056  bu.  of  Indian  corn  produced  in 
this  country  in  one  year  was  2^<>lo  more  than  the  number 
of  bushels  of  wheat.    How  much  wheat  was  produced  ? 

23.  The  average  price  of  hay  in  Kansas  recently  was 
only  $4.06  a  ton,  which  was  23  J  %  as  much  as  in  Massa- 

^       chusetts.    What  was  the  price  in  Massachusetts,  and  why 
was  there  this  great  difference? 

24.  When  the  hay  crop  of  the  country  is  60  million  tons, 
worth  $7.50  a  ton,  what  is  the  value  of  the  whole  crop? 
If  the  crop  of  New  York,  the  chief  hay-producing  state,  is 
worth  10%  of  this  amount,  what  is  its  value? 

25.  In  one  of  the  states  2.2  million  acres  produced  74.8 
million  bushels  of  oats  in  one  year,  worth  $18,700,000. 
What  was  the  average  yield  per  acre,  the  average  price 
per  bushel,  and  the  average  value  of  the  crop  per  acre  ? 

26.  When  the  annual  products  of  the  155,000  farms  in 
Minnesota  were  worth  $170,500,000,  what  was  the  average 
per  farm? 

27.  Of  these  farms,  if  6,500,000  acres  produced  97,500,000 
bu.  of  wheat,  what  was  the  average  yield  per  acre  ?  What 
was  the  total  yield  worth  at  60/  a  bushel  ? 

28.  Some  of  this  grain  went  to  Duluth,  where  an  eleva- 
tor distributed  20,000  bu.  of  wheat  to  a  ship  in  one  hour. 
Allowing  62  lb.  to  the  bushel,  how  many  tons  did  it  dis- 
tribute in  a  minute  ? 

J.  29.  If  one  elevator  spout  carries  8602^J  bu.  of  wheat  in 
an  hour,  how  long  will  it  take  a  6-spout  elevator  to  unload 
a  train  of  40  cars,  averaging  20  tons  to  a  car,  allowing  62  lb. 
to  the  bushel,  no  allowance  being  made  for  moving  the  cars  ? 


REVIEW  131 


ORAL   EXERCISE 


1.  At  $26  a  ton,  what  is  the  cost  of  200  lb.  of  bone 
meal?  of  50  lb.  ? 

2.  At  $26  a  ton,  what  is  the  cost  of  100  lb.  of  cotton- 
seed meal  ?  of  500  lb.? 

3.  At  $12.50  a  ton,  what  is  the  cost  of  100  lb.  of  acid 
phosphate?  of  400  lb.? 

4.  At  $1.35  per  100  lb.,  what  is  the  cost  of  a  ton  of 
bone  meal?   of  300  lb.  ? 

5.  At  $48  a  ton,  what  does  1  lb.  of  nitrate  of  soda  cost? 
What  is  the  cost  of  100  lb.  ? 

6.  At  $125  a  ton,  what  is  the  cost  of  200  lb.  of  sul- 
phate of  copper?  of  100  lb.? 

7.  At  $2.50  per  100  lb.,  what  is  the  cost  of  a  ton  of 
nitrate  of  soda?   of  250  lb.? 

8.  At  $2.20  per  100  lb.,  what  is  the  cost  of  a  ton  of 
muriate  of  potash  ?   of  500  lb.  ? 

9.  At  $2.60  per  100  lb.,  what  is  the  cost  of  a  ton  of 
sulphate  of  potash  ?   of  500  lb.? 

10.  If  nitrate  of  soda  contains  15%  nitrogen,  what  is 
the  weight  of  nitrogen  in  a  ton  ? 

11.  At  $3.30  per  100  lb.,  what  is  the  cost  of  a  ton  of 
sulphate  of  ammonia?   of  600  lb.? 

12.  If  acid  phosphate  contains  14%  phosphoric  acid, 
what  is  the  weight  of  phosphoric  acid  in  a  ton  ? 

13.  A  certain  fertilizer  for  tobacco  land  is  made  of 
900  lb.  cotton-seed  meal  @  $1.30  per  1001b.,  100  lb.  nitrate 
of  soda  @  $50  per  ton,  250  lb.  sulphate  of  potash  @  $2.50 
per  100  lb.,  750  lb.  acid  phosphate  @  60/  per  100  lb. 
What  is  the  cost  of  each  ingredient  ? 


132  REVIEW 


WRITTEN  EXERCISE 


1.  To  lessen  potato  scab  the  seed  potatoes  are  soaked  in 
a  solution  of  J  pt.  of  formalin  to  15  gal.  of  water.  What 
is  the  per  cent  of  formalin  in  the  mixture?  What  is  the 
per  cent  of  water  ? 

2.  Bordeaux  mixture,  for  spraying,  contains  1^^  by 
weight  of  copper  sulphate,  li%  of  unslacked  lime,  and  the 
rest  water.  How  many  pounds  of  each  in  a  barrel  contain- 
ing 250  lb.  of  the  mixture  ? 

3.  Half  of  a  peach  tree  was  sprayed  with  Bordeaux  mix- 
ture and  the  other  half  was  not.  From  the  sprayed  half 
284.8  lb.  of  fruit  were  taken,  and  from  the  other  half  95% 
less.    How  many  pounds  were  taken  from  the  tree? 

4.  If  only  the  fiber  (lint)  is  taken  from  the  land,  a  cotton 
crop  removes  from  the  soil  only  S.6(/o  as  much  plant  food 
as  a  wheat  crop.  The  wheat  crop  takes  32.4  lb.  a  year 
from  each  acre.  What  is  the  weight  of  plant  food  that  a 
cotton  crop  takes  each  year  from  a  50-acre  field  ? 

5.  It  is  estimated  that  a  chickadee  will  destroy  30  egg- 
laying  cankerworm  moths  during  each  of  the  25  days  that 
these  moths,  which  are  wingless,  crawl  up  orchard  trees. 
This  would  result  in  the  destruction  of  how  many  eggs 
by  a  single  chickadee  in  an  orchard,  if  each  moth  would 
have  laid  185  eggs  ? 

''  6.  A  farmer  by  placing  a  burlap  band  around  an  apple 
tree  caught  96  larvae  of  the  coddling  moth  in  a  week.  Sup- 
pose each  of  these  had  emerged  from  its  cocoon  as  a  moth, 
had  deposited  an  egg  on  each  of  294  apples,  each  egg 
hatching  into  an  apple-tree  worm  and  destroying  the  apple, 
how  many  apples  would  have  been  saved  by  destroying 
these  96  larvae  ? 


FARM  PROBLEMS  133 

7.  If  bone  meal  is  4%  nitrogen,  and  nitrate  of  soda  is 
15%  nitrogen,  how  many  pounds  of  nitrogen  in  a  ton  of 
each?    in  1500  lb.? 

8.  In  a  certain  fertilizer  (plant  food)  for  land  on  which 
corn  is  grown,  43f  %  is  acid  phosphate,  47^%  is  cotton- 
seed meal,  and  the  rest  is  kainit.  How  many  pounds  of 
each  to  a  ton  ? 

9.  In  a  certain  fertilizer  for  land  on  which  cotton  is 
grown,  53|%  is  acid  phosphate  and  the  rest  is  32  parts 
fish  scrap  to  5  parts  muriate  of  potash.  How  many  pounds 
of  each  to  a  ton? 

10.  A  farmer  used  the  following  fertilizer  for  an  acre  of 
grapes  :  300  lb.  acid  phosphate  @  $11.50  a  ton,  the  same 
weight  of  bone  meal  @  $26.50  a  ton,  and  the  same  weight 
of  muriate  of  potash  @  $42.50  a  ton.  What  did  the  fer- 
tilizer cost  ? 

11.  A  Virginia  tobacco  grower  used  for  his  land  a  ferti- 
lizer composed  of  35%  cotton-seed  meal,  5%  nitrate  of  soda, 
and  the  rest  of  sulphate  of  potash  and  acid  phosphate  in 
the  ratio  of  1  to  3.  How  many  pounds  of  each  in  750  lb.  ? 
in  1  T.  ?   in  1 J  T.  ? 

12.  A  farmer  mixed  a  ton  of  fertilizer  for  his  corn  land, 
using  half  cotton-seed  meal  @  $24.60  a  ton  and  the  rest 
acid  phosphate  and  muriate  of  potash  in  the  ratio  of  19 
to  1.  The  acid  phosphate  cost  $11.50  a  ton,  and  the  muriate 
of  potash  $42.50  a  ton.    What  did  the  fertilizer  cost? 

13.  A  cotton  planter  mixed  a  ton  of  fertilizer  for  his 
land,  using  half  acid  phosphate  @  $11.50  a  ton  and  the 
rest  cotton-seed  meal  and  muriate  of  potash  in  the  ratio  of 
37  to  3.  The  cotton-seed  meal  cost  $24.60  a  ton  and  the 
muriate  of  potash  $42.50  a  ton.  What  did  the  fertilizer 
cost? 


134  REVIEW 

14.  A  market  gardener  used  the  following  fertilizer  for 
3  acres  of  vegetables  :  400  lb.  nitrate  of  soda  @  $48  a  ton, 
900  lb.  cotton-seed  meal  @  $24.60  a  ton,  900  lb.  acid  phos- 
phate @  $11.70  a  ton,  900  lb.  bone  meal  @  $26.10  a  ton, 
and  33^%  less  muriate  of  potash  than  bone  meal  @  $2.15 
per  100  lb.    What  did  the  fertilizer  cost  per  acre  ? 

15.  A  gardener  used  700  lb.  of  fertilizer  per  acre,  com- 
posed of  1  part  nitrate  of  soda  to  2  parts  each  of  acid  phos- 
phate, bone  meal,  and  muriate  of  potash.  The  nitrate  of 
soda  cost  $48  a  ton,  the  acid  phosphate  $11.50  a  ton,  the 
bone  meal  $2.15  per  100  lb.,  and  the  muriate  of  potash 
$42.50  a  ton.    What  did  the  fertilizer  cost  for  5  acres  ? 

16.  Of  an  Iowa  farm  of  160  acres,  10%  was  swampy. 
Before  this  part  was  properly  drained  it  yielded  some  hay, 
averaging  in  value  $3.25  to  the  acre.  After  being  drained 
and  tiled  it  yielded  grain  to  the  value  of  $12  to  the  acre. 
What  was  the  per  cent  of  increase  in  productiveness  of  this 
part  of  the  farm  after  it  was  drained? 

17.  By  a  proper  selection  of  seed  corn  for  three  years,  a 
farmer  was  finally  able  to  grow  80  bu.  of  corn  on  one  acre. 
On  an  adjoining  acre  with  similar  soil  where  seed  was 
taken  at  random,  the  yield  was  33 J  bu.  If  he  had  followed 
the  first  plan  instead  of  the  second  for  all  of  his  52  acres, 
what  would  have  been  the  per  cent  of  gain? 

18.  On  a  piece  of  average  ground  a  farmer  counted  22 
heads  of  smutty  wheat  out  of  a  total  of  176  heads.  If  the 
yield  was  16  bu.  of  good  wheat  to  the  acre,  and  the  tract 
contained  42  acres,  what  was  the  farmer's  loss  in  yield? 
By  treating  a  certain  area  with  formalin  he  killed  all  the 
smut  spores,  and  by  selecting  his  seed  from  these  healthy 
plants  he  afterwards  grew  all  of  his  wheat  free  from 
disease.   What  was  now  the  yield  per  acre? 


FARM  PROBLEMS  135 

19.  A  cow  gives  875  lb.  of  milk  in  a  certain  month.  The 
milk  tests  4.3%  butter  fat.  How  many  pounds  of  butter 
fat  does  she  produce  in  this  month? 

20.  If  the  butter  fat  is  sufficient  for  ^  more  than  its 
weight  of  butter,  how  many  pounds  of  butter  could  be 
made  from  the  milk  mentioned  in  Ex.  19  ? 

21.  If  the  butter  mentioned  in  Ex.  20  is  sold  at  24/  a 
pound,  what  is  the  value  of  the  butter  produced  in  this 
month  from  the  milk  of  this  cow? 

22.  A  man  has  a  dairy  that  produces  milk  averaging 
3.75%  butter  fat  during  a  certain  month.  The  butter  fat 
weighs  78 7 J  lb.    How  many  pounds  of  milk  are  produced? 

23.  The  weight  of  the  solid  matter  in  the  milk  of  a 
certain  dairy  during  a  summer  was  12^%  of  the  total 
weight,  and  the  butter  fat  was  25%  of  the  solids.  The 
butter  fat  was  what  per  cent  of  the  weight  of  the  milk? 

24.  The  weight  of  the  solid  matter  in  the  milk  of  a  cer- 
tain dairy  during  June  was  13.2  %  of  the  total  weight,  and 
the  butter  fat  was  J  of  the  solids.  How  many  pounds  of 
butter  fat  to  a  ton  of  milk? 

25.  A  farmer  bought  24  cattle  and  sold  them  a  year  and 
a  half  later  for  $1200.  He  estimated  his  net  gain  at  $10  a 
head,  20%  of  which  was  due  to  extra  care  in  feeding.  What 
would  have  been  the  average  selling  price  per  head  if  he 
had  not  taken  this  extra  care?     . 

26.  A  farmer  has  two  cows,  one  supplying  1000  lb.  of 
milk  in  a  certain  month,  testing  3%  butter  fat,  and  the 
other  800  lb.,  testing  4%  butter  fat.  If  the  butter  fat  is 
sufficient  for  116§%  of  its  weight  in  butter,  and  butter  is 
worth  23/  a  pound,  which  cow  pays  the  farmer  the  more  for 
that  month,  the  feed  costing  the  same?    How  much  more? 


136 


REVIEW 


27.  The  books  of  a  creamery  show  the  following  record 
for  seven  of  its  patrons,  A,  B,  C,  D,  E,  F,  G,  for  six  days. 
The  figures  represent  the  pounds  of  cream  delivered  each 
day,  and  the  per  cent  of  butter  fat  in  the  cream,  as  shown 
by  tests. 


A 

B 

c 

D 

E 

F 

G 

Feb.  2. 

27 

21 

41 

18 

24 

59 

78 

«    3. 

26 

28 

42 

19 

34 

67 

81 

"    4 

23 

30 

45 

16 

38 

72 

90 

"    6. 

25 

32 

47 

20 

'39 

76 

91 

«     6. 

28 

35 

50 

21 

38 

72 

89 

«     7. 

23 

39 

52 

20 

39 

75 

92 

Per  cent  of 
butter  fat 

29% 

34% 

27% 

30% 

26% 

35% 

32% 

How  many  pounds  of  cream  were  supplied  by  each  patron  ? 
Of  this  amount  how  many  pounds  were  butter  fat  ?  If  this 
butter  fat  was  sufficient  for  116f  %  of  its  weight  in  butter, 
and  the  patrons  received  24/  per  pound  of  butter,  what 
did  each  receive  for  the  six  days  ? 

28.  One  day's  report  of  a  creamery  operating  five  stations 
shows  the  pounds  of  milk  and  cream  received,  as  follows: 

Sta.  1         Sta.  2        Sta.  3        Sta.  4        Sta.  5 
Milk         1032         1152         864         720         1008 
Cream         500  480         384         288  360 

a.  If  16f  %  of  the  milk  is  cream,  how  many  pounds  of 
cream  has  each  station  ? 

h.  If  2h^o  of  t^6  cream  is  butter  fat,  how  many  pounds 
of  butter  fat  has  each? 

c.  If  the  butter  fat  is  sufficient  for  116§%  of  its  weight 
in  butter,  how  many  pounds  of  butter  does  each  produce  ? 

d.  What  is  the  butter  of  each  worth  at  23/  a  pound? 

e.  Show  that  the  total  number  of  pounds  of  butter  is  819. 


FARM  PROBLEMS  13T 

29.  A  certain  creamery  uses  6400  lb.  of  milk  in  a  week. 
The  skim  milk  amounts  to  80%  of  the  whole  milk,  and 
tests  f  %  butter  fat.  How  many  pounds  of  butter  fat  are 
lost  in  the  skim  milk?  If  this  would  suffice  for  16§% 
more  than  its  weight  in  butter,  how  much  butter  is  lost  ? 

30.  A  cow  gives  850  lb.  of  milk  in  a  certain  month. 
After  the  butter  fat  is  extracted  the  milk  weighs  816  lb. 
What  per  cent  of  butter  fat  did  the  milk  yield?  How 
many  pounds?  How  many  pounds  of  butter  could  be  made 
from  it,  the  butter  weighing  116^(^o  as  much  as  the  fat? 
What  would  this  butter  be  worth  at  25^  sl  pound  ? 

31.  An  Illinois  farmer  made  a  fertilizer  for  his  corn- 
fields, using  95  parts  acid  phosphate,  100  parts  cotton-seed 
meal,  and  5  parts  muriate  of  potash.  He  then  decided 
to  add  enough  acid  phosphate  to  100  lb.  of  the  mixture 
to  make  it  50%  of  the  total.    How  much  did  he  add? 

If  he  adds  x  lb.,  then  50%  of  (100  +  x)  lb.  =  47i  lb.  -h  x  lb.  Hence 
2  J  =  i  X,  and  x  =  5. 

32.  A  Louisiana  planter  has  some  fertilizer  for  his  cot- 
ton fields,  consisting  of  62^(fo  acid  phosphate,  30%  dried 
blood,  7J%  muriate  of  potash.  He  finds  that  his  land 
needs  more  acid  phosphate,  and  decides  to  add  enough  of 
it  to  the  mixture  so  that  it  shall  be  70%  of  the  total. 
How  many  pounds  of  acid  phosphate  must  he  add  to  a 
ton  of  the  fertilizer  ? 

33.  A  North  Carolina  farmer  finds  that  a  fertilizer  that 
he  has  been  using  is  too  rich  in  acid  phosphate.  The 
formula  used  is  25%  dried  blood,  5%  nitrate  of  soda,  20% 
sulphate  of  potash,  and  the  rest  acid  phosphate.  How 
many  pounds  less  of  acid  phosphate  must  he  use  to  every 
400  lb.  of  sulphate  of  potash,  so  that  the  acid  phosphate 
shall  be  45%  of  the  mixture? 


CHAPTER   II 

I.    BUSINESS  APPLICATIONS 
GOING  INTO  BUSINESS 

108.  How  a  boy  may  go  into  business.  If  a  boy  on  leaving 
school  goes  into  some  trade,  he  will  start  with  very  low 
wages.  He  may  be  employed  to  go  on  errands,  to  wrap  up 
goods,  or  to  deliver  parcels.  He  will  soon  show  whether 
he  has  any  elements  of  success.  If  he  shirks  work,  indulges 
in  too  much  talk,  watches  the  clock  for  closing  time,  and 
wastes  what  money  he  receives,  he  will  either  be  ^^out  of 
a  job  "  or  be  left  in  the  lowest  kind  of  place. 

But  if  he  works  his  best,  exerts  himself  to  be  helpful  in 
every  way,  is  always  a  gentleman,  and  takes  an  interest  in 
improving  his  work,  he  will  soon  begin  to  work  his  way  up. 
If  he  saves  money,  shows  himself  a  good  manager^  earns  a 
reputation  for  absolute  truth,  and  has  a  circle  of  customers 
who  know  they  can  always  rely  upon  him,  he  will  probably 
succeed  in  business  for  himself.  These  are  the  qualities 
that  make  great  merchants  and  manufacturers.  The  world 
is  waiting  for  such  men. 

109.  How  a  girl  may  go  into  business.  The  girl  who  has 
to  support  herself  may  begin  as  cash  girl  or  clerk  in  a  store 
and  work  up  to  the  position  of  buyer  in  some  department. 
If  she  is  in  a  factory,  a  position  as  overseer  is  among  the 
possibilities.  If  she  is  a  stenographer,  good  positions  are 
always  awaiting  capable  women,  often  demanding  consider- 
able knowledge  of  the  business  with  which  they  are  con- 
nected. If  she  marries,  some  knowledge  of  business  is 
equally  as  important,  for  many  homes  are  made  unhappy 
because  of  lack  of  this  knowledge. 

138 


INCOMES 


139 


WRITTEN   EXERCISE 

1.  If  a  man's  salary  was  decreased  2j%  and  was  then 
$1170  a  year,  how  much  was  it  before  the  decrease  ? 

2.  If  a  man's  salary  was  increased  5%  and  was  then 
$1207.50  a  year,  how  much  was  it  before  the  increase? 

3.  If  you  work  312  days  in  a  year,  at  $1.75  a  day,  and 
save    $91,   what 
per  cent  of  your 


do 


you 


income 
spend? 

4.  An  agent's 
bill  for  goods 
bought,  plus  his 
commission  of 
2%,  is  $1377. 
What  did  the 
goods   cost  ? 

5.  If  you  worked  at  a  salary  of  $1.25  a  day,  and  spent 
80%  of  your  income  for  living  expenses,  and  saved  $75  in 
a  year,  how  many  days  did  you  work  ? 

6.  If  you  should  work  310  days  in  a  year,  and  spend 
82^%  of  your  income  for  living  expenses,  how  much  would 
you  have  to  earn  a  day  in  order  to  save  $108.50  a  year  ? 

7.  A  boy  is  offered  a  salary  of  $7.50  a  week  for  the  first 
year  in  a  store,  33^%  more  the  second  year,  and  50% 
beyond  that  thereafter.  What  will  be  the  total  salary  for 
3  years,  allowing  52  weeks  to  the  year  ? 

8.  If  a  carpenter  earns  $3  a  day  and  works  300  days  in 
one  year,  what  will  be  the  alteration  in  annual  income  if 
his  daily  wages  are  increased  10%  the  following  year  and 
the  working  days  are  decreased  10%  in  number? 


140  GOING  INTO  BUSINESS 

9.  A  boy  who  has  been  working  this  year  at  $25  a  month 
is  offered  either  an  increase  of  20%  for  next  year  or  a 
salary  of  $7  a  week.  Which  will  bring  the  more  income, 
and  how  much  more  per  year?    (Use  52  wk.) 

10.  A  girl  who  has  been  working  in  a  factory  at  $21.67 
a  month,  is  offered  an  increase  of  10%  where  she  is  or  a 
salary  of  $5.60  a  week  elsewhere.  Which  will  bring  the 
more  income,  and  how  much  more  per  year?  (Use  52  wk.) 

11.  A  boy  went  to  work  at  90/  a  day.  The  second  year 
his  wages  were  increased  20%,  the  third  year  they  were 
42/  a  day  more  than  the  second,  and  the  fourth  they  were 
increased  33i%.  At  300  working  days  to  the  year,  what 
was  his  total  income  for  each  year  ? 

12.  A  girl  entering  a  trade  school  finds  that  graduates 
from  the  dressmaking  department  receive  on  an  average 
$4.60  a  week  the  first  year ;  those  from  the  millinery  de- 
partment, 5%  less;  those  from  the  embroidery  department, 
5%  more  than  the  dressmakers;  and  those  from  the  oper- 
ating department,  66^ ^o  3-s  much  as  the  last  two  together. 
Find  the  average  wages  of  each,  and  tell  which  depart- 
ment the  girl  probably  entered.    (Use  52  wk.) 

13.  A  girl  leaving  the  public  school  finds  she  can  enter 
a  city  shop  at  a  salary  of  $3  a  week  the  first  year,  with 
16|%  more  the  second  year,  and  a  14f  %  increase  the 
third  year.  Instead  of  this  she  enters  a  trade  school  for  a 
year,  tuition  free.  She  then  receives  a  salary  of  $5  a  week 
the  first  year  and  20%  more  the  second  year.  Counting 
50  working  weeks  a  year,  how  much  more  does  she  receive 
in  three  years  by  the  plan  she  follows  after  leaving  the 
public  school  than  she  would  have  received  without  the 
trade-school  training  ? 


BANK  ACCOUNTS  141 


BANK  ACCOUNTS 


110.  A  bank  account  essential.  One  thing  essential  to  any 
one  who  hopes  to  succeed  is  a  bank  account.  Any  one  may 
"  open  an  account,"  as  it  is  called,  as  soon  as  he  begins  to 
save  even  a  small  amount.  In  most  parts  of  the  country 
small  sums  are  usually  deposited  in  savings  banks. 

111.  The  savings  banks.  To  deposit  money  a  person  simply 
goes  to  the  bank,  says  that  he  wishes  to  open  an  account, 
and  leaves  his  money  with  the  officer  in  charge.  The  officer 
gives  him  a  book  in  which  the  amount  is  written,  and  the 
depositor  writes  his  name  in  a  book  of  signatures,  for 
identification.  When  he  wishes  to  draw  out  any  money, 
he  takes  his  book  to  the  bank,  states  how  much  he  wishes, 
signs  a  receipt  (in  some  parts  of  the  country  he  makes  out 
a  check),  has  the  amount  entered  in  his  book,  and  the 
money  is  paid  to  him  if  it  does  not  exceed  his  deposits,  — 
his  "  balance,"  as  they  say.  If  he  forms  the  habit  of  depos- 
iting money  when  he  has  any  to  spare,  and  never  drawing 
except  in  an  emergency,  he  will  be  surprised  to  see  how  it 
accumulates. 

WRITTEN   EXERCISE 

1.  What  does  25  ct.  saved  a  day  amount  to  in  a  year  ? 

2.  How  much  will  15  ct.  a  day,  310  days  a  year,  amount 
to  in  10  years,  not  counting  interest  ? 

3.  If  a  boy,  beginning  when  he  is  16,  saves  25  ct.  a  day 
for  300  days  a  year,  and  deposits  it  in  a  savings  bank,  how 
much  will  he  have  when  he  is  21,  not  counting  interest? 

4.  If  a  father  gives  his  daughter  $1  when  she  is  1  yr. 
old,  $2  on  her  next  birthday,  and  so  on  until  she  is  21, 
depositing  it  for  her  in  a  savings  bank,  how  much  will  she 
have  when  she  is  21,  not  counting  interest  ? 


142  BANK  ACCOUNTS 

5.  A  man  saves  on  an  average  2b f^  a  day  the  first  year 
he  works  on  a  certain  farm,  and  120%  as  much  the  second 
year,  depositing  it  in  a  savings  bank.  If  he  works  306  days 
each  year,  how  much  does  he  save  in  the  two  years? 

6.  A  farmer's  savings-bank  deposits  average  $25  a  month 
during  a  certain  year,  and  97%  as  much  during  the  next 
year.  The  year  following  he  deposited  110%  as  much  as 
he  did  the  second  year.  How  much  did  he  deposit  during 
the  three  years  ? 

7.  If  a  man  saved  $1  a  week  during  the  year  in  which 
he  was  21,  and  increased  his  savings  each  year  by  10%  on 
the  amount  of  the  preceding  year,  and  worked  50  weeks  a 
year,  how  much  would  he  save  during  the  year  in  which 
he  was  29  years  old? 

8.  A  merchant  saves  $375  the  first  year  he  is  in  busi- 
ness. The  second  year  he  increases  his  savings  one  third. 
The  third  year  they  are  only  85%  as  much  as  the  second 
year.  The  fourth  year  they  increase  30%.  How  much  does 
he  save  in  the  four  years  ? 

9.  A  man  works  on  a  salary  of  $15  a  week  for  50  weeks 
in  a  year.  His  expenses  are  $15  a  month  for  house  rent, 
60%  as  much  for  clothing,  300%  as  much  for  food  as  for 
clothing,  and  20%  as  much  for  other  necessary  expenses 
as  for  food.  How  much  of  his  salary  can  he  reserve  for 
the  savings  bank? 

10.  A  clerk  in  a  store  had  a  salary  of  $12  a  week  two 
years  ago,  and  a  commission  of  2%  on  the  goods  sold  by 
him.  That  year  he  worked  48  weeks  and  sold  $2350  worth 
of  goods.  Last  year  his  salary  was  increased  2b(fo,  his 
commissions  remaining  the  same.  He  worked  49  weeks 
and  sold  $2750  worth  of  goods.  How  much  was  his  income 
increased  ? 


COMPOUND  INTEREST 


143 


112.  How  savings  banks  pay  interest.  Savings  banks  usually 
pay  interest  every  six  months.  This  is  added  to  the  prin- 
cipal, and  the  amount  draws  interest. 

113.  Compound  interest.  When  the  interest  is  added  to 
the  principal  as  it  becomes  due,  and  the  amount  draws 
interest,  the  owner  is  said  to  receive  compound  interest. 

Compound  interest  is  no  longer  allowed  on  notes.  But  if  any 
one  collects  his  interest  when  due, 
and  at  once  reinvests  it,  of  course 
he  practically  has  the  advantage  of 
compound  interest.  The  method 
of  finding  compound  interest  is 
substantially  the  same  as  that  used 
in  simple  interest. 

114.  Illustrative  problem.   Ee- 

quired  the  amount  of  $2000 
invested  in  a  savings  bank  at 
4%  annually,  the  interest  com- 
pounded semiannually,  for  2 
years. 

The  simple  interest  for  the  same 
length  of  time  is  ^160,  $4.87  less 
than  the  compound  interest.  $2164.87  =  amt.  after  2  yr. 


$2000       = 
.02 

first  principal 

40       = 
2000 

:  first  interest 

2040       = 
.02 

:  amt.  after  6  mo. 

40.80  = 
2040 

:  int.  second  6  mo. 

2080.80  = 
.02 

:  amt.  after  1  yr. 

41.62  = 
2080.80 

:  int.  third  6  mo. 

2122.42  = 
.02 

:  amt.  after  1\  yr. 

42.45  = 
2122.42 

:  int.  fourth  6  mo. 

ORAL  EXERCISE 

Find  the  amount  at  compound  interest : 
1.    $1000,  2  yr.,  4%.  2.    $1000,  2  yr.,  5%. 

In  Ex.  1  we  have  $40  interest  each  year,  plus  4%  of  $40. 
3.    $2000,  2  yr.,  4%.  4.    $2000,  2  yr.,  5%. 

5.    $3000,  2  yr.,  3%.  6.    $3000,  2  yr.,  2%. 

7.    $5000,  2  yr.,  4%.  8.    $5000,  2  yr.,  3%. 

e.    $8000,  2  yr.,  5%.  10.    $10,000,  2  yr.,  4%. 


144  BANK  ACCOUNTS 

WRITTEN  EXERCISE 

Find  the  amount  at  simple  interest^  and  at  interest 
compounded  annually: 

1.  $2500,  4  yr.,  5%.  2.  $4000,  3  yr.,  6%. 

3.  $3500,  3  yr.,  4%.  4.  $2250,  4  yr.,  3%. 

5.  $2750,  4  yr.,  3%.  6.  $1750,  3  yr.,  3^%. 

7.  $625.50,  4  yr.,  31%.  8.  $10,000,  6  yr.,  4%. 

9.  $425.50,  4  yr.,  41%.  10.  $275.50,  3  yr.,  4^%. 

Find  the  amount  of  principal  and  interest^  the  interest 
being  compounded  semiannually: 

11.    $200,  3  yr.,  4%.  12.  $300,  2  yr.,  4%. 

13.    $650,  2  yr.,  6%.  14.  $700,  3  yr.,  3%. 

15.    $800,  3  yr.,  4%.  16.  $500,  2  yr.,  4%. 

17.    $1000,  2  yr.,  4i%.  18.  $1000,  3  yr.,  4%. 

19.    $2000,  2  yr.,  3J%.  20.  $3000,  2  yr.,  2^%. 

21.  Which  brings  the  more  interest  in  2  yr.,  on  $1250, 
4%  in  a  savings  bank,  compounded  semiannually  (the  money 
being  deposited  at  the  beginning  of  the  year),  or  4J% 
simple  interest? 

22.  If  a  man  on  January  1  deposited  $2000  in  a  savings 
bank,  and  left  it  for  2  yr.,  at  4%,  the  interest  being  com- 
pounded semiannually,  how  much  less  interest  would  he 
receive  than  by  loaning  it  at  5%  simple  interest? 

23.  If  a  man  deposits  in  a  savings  bank  $200  Jan- 
uary 1,  $300  February  1,  $100  May  1,  $400  August  1,  and 
$350  November  1,  and  the  rules  of  the  bank  allow  4% 
interest  on  all  of  these  sums,  compounding  it  on  July  1 
and  January  1,  how  much  will  the  man  have  to  his  credit 
on  the  January  1  following  these  deposits? 


BANKS  OF  DEPOSIT 


145 


115.  Banks  of 
deposit.  When  a 
man  has  money 
enough  ahead  to 
paj  his  bills  by 
checks,  he  will 
need  to  have  an 
account  with  an 
ordinary  bank, 
sometimes  called 
a  hank  of  deposit. 

Such  banks  do 
not  pay  interest 
on  small  accounts, 
deposit  being  a  matter  of 
convenience  and  safety. 
If  a  man  wishes  to  open 
an  account,  he  sometimes 
has  to  give  references,  for 
banks  do  not  wish  to  do 
business  with  unreliable 
people. 

116.  Deposit  slips. 

When  a  man  deposits 
money  he  makes  out 
a  deposit  slip,  as  here 
shown,  and  leaves  it 
at  the  bank. 


the 


SECOND    NATIONAL   BANK 

BOSTON.   MASS. 
Deposited  for  the  account  of 

Date 

19... 

Bills  and  small  coin     .     . 

Gold 

Silver 

Check  on Bank 

* 

Total 

ORAL  EXERCISE 

Tell  the  sum  of  each  of  the  following  lists  of  deposits  : 

1.    $15.50  2.    $12.75  3.    $23.80         4.    $12.00 

3.75  2.25  12.70  13.75 


146  BANK  ACCOUNTS 


WRITTEN  EXERCISE 


Make  out  deposit  slips  for  the  following  deposits^  nam- 
ing some  bank  in  your  town: 

1.  Bills,  $254;  silver,  $40;  checks  on  First  National 
Bank,  $87.50;  Traders  Bank,  $127.50. 

2.  Bills,  etc.,  $423.57;  gold,  $275;  silver,  $135.75; 
check  on  Cotton  Exchange  Bank,  $342.60. 

3.  Bills,  etc.,  $135.50;  checks  on  Chemical  National 
Bank  of  New  York,  $325;  Third  National,  $63. 73, 

4.  Bills,  etc.,  $1726.45 ;  gold,  $125  ;  silver,  $100;  checks 
on  Traders  Bank,  $335.50 ;  Second  National,  $175.40. 

5.  Bills,  etc.,  $262.75;  checks  on  Garfield  National, 
$96.50,  $200;  Jefferson  and  Lee  National,  $325,  $46.50. 

6.  Gold,  $50;  checks  on  First  National,  $27.62, 
$41.75,  $32.80;  Lincoln  Trust  Company,  $37.42,  $21.85. 

7.  Bills,  etc.,  $146.73  ;  silver,  $275  ;  checks  on  Miners 
National  Bank,  $43.50;  Eocky  Mountain  National,  $250. 

8.  Bills,  $145;  silver,  $350;  gold,  $480;  checks  on 
Merchants  National  Bank,  $255 ;  Farmers  Trust  Company, 
$162.50;  Second  National  Bank,   $275.50. 

9.  A  merchant  deposited  $175.80  in  cash  to-day,  and  a 
check  for  25%  of  a  debt  of  $176  due  him,  and  a  check  in 
payment  for  18f  yd.  of  velvet  at  $2.16  a  yard  less  33i% 
on  account  of  a  bargain  sale.    Make  out  a  deposit  slip. 

10.  A  jeweler  received  cash  for  the  following:  3  doz. 
forks  @  $16.50 ;  4i-  doz.  teaspoons  @  $15  ;  a  watch  @ 
$32.75  ;  and  2  clocks  @  $6.75.  He  also  received  checks  on 
the  First  National  Bank  for  the  following :  2\  doz.  table 
spoons  @  $19.50  ;  3  doz.  dessert  spoons  @  $17.75  ;  and  9 
nut  crackers  @  $9  a  dozen.    Make  out  a  deposit  slip. 


CHECK  BOOKS 


147 


117.  Check  books.    A  check  hook  is  given  the  depositor. 
Each  page  has  one  or  more  checks  and  stubs. 


Stub 


Check 


No.  i'/^ 

Date 

To/.  //.  ^■Jn.iM 
For  ^0.1.  a^m^t. 
Amt.  $/o,'^ 


No.  £/6'  Chicago,  III.,  [Date] 19 

FIRST  NATIONAL  BANK  OF  CHICAGO 

Pay  to  the  order  of 


&i/lt&&'yu  a^ncL  ^ 


Dollars 


118.  Payee.   The  person  to  whom  a  check  is  payable  is 
called  the  payee.    A  check  is  usually  made  payable  to : 

1.  "  Self/^  in  which  case  the  drawer  alone  can  collect  it. 

2.  The  order  of  the  payee,  when  the  payee  must  indorse  it. 

3.  The  payee  or  bearer,  when  any  one  can  collect  it. 

4.  "  Cash,"  in  which  case  any  one  can  collect  it. 


ORAL  EXERCISE 


Given  the  following  deposits  and  checks^  tell  the  balance: 


Deposits  Checks 

1.    $25  $15 

70  27 

32  42 


Deposits 

2.  $37 
41 
20 


Checks 

$19 
32 
15 


Deposits  Checks 

3.    $48  $20 

27  15 

13  17 


4.  $62 

$37 

5.  $75 

$62 

6.  $50 

$65 

48 

41 

25 

17 

40 

30 

17 

20 

32 

40 

75 

50 

148  BANK  ACCOUNTS 

WRITTEN  EXERCISE 

1.  If  your  deposits  in  a  bank  have  been  $14.75,  $32, 
$15,  $25,  $50,  $75,  $1.75,  and  you  have  drawn  checks  for 
$9.50,  $18.75,  $30,  what  is  your  balance? 

2.  A  man  earning  $15  a  week  deposits  $12  every  Satur- 
day, and  on  each  Monday  gives  a  check  for  $6  for  his  board. 
What  will  be  his  balance  in  6  months  (26  weeks)? 

3.  If  your  deposits  in  a  bank  have  been  $32.75,  $49.63, 
$2S,  $14.90,  $25,  $10,  $30,  $42.75,  $71.25,  and  you 
have  drawn  checks  for  $5.75,  $13.50,  $32,  $4.50,  $36.50, 
$52.80,  what  is  your  balance  ? 

4.  A  farmer  having  $275.60  in  the  bank  deposits  dur- 
ing the  next  six  months  $23.50,  $17.42,  $75,  $32.40,  and 
the  proceeds  of  the  sale  of  7  cows  @  $37.50  less  5%.  He 
gives  checks  for  $17.92,  $8.50,  $72.80,  $9.50,  $6.75, 
$13.90,  and  $26.50.    What  is  his  balance? 

5.  A  merchant's  deposits  this  week  have  been  $127.42, 
$135,  $72.50,  $265.75,  $327.40,  $182.50,  and  he  has  drawn 
checks  for  $236.50,  $15.75,  $27.90,  $241.60,  and  $29.50. 
He  has  also  paid  by  check  a  bill  for  $176.70  less  10%,  and 
another  for  $75.25  less  10%,  3%.  At  the  beginning  of  the 
week  he  had  $475.80  in  the  bank.  What  is  his  balance  at 
the  end  of  the  week  ? 

6.  A  merchant's  deposits  this  week  have  been  $261.50, 
$392.75,  $62.40,  $112.30,  $98.76,  $115,  and  he  has  drawn 
checks  for  $42.80,  $174.95,  $162.30,  $81.50,  $15,  $27.40, 
and  $37.50.  He  Jias  also  given  a  check  for  $125  plus  6 
months'  interest  at  5%,  and  one  in  payment  of  a  bill  for 
$248.50  less  S%,  5%.  At  the  beginning  of  the  week  he 
had  $692.80  in  the  bank.  What  is  his  balance  at  the  end 
of  the  week  ? 


BORROWING  FROM  A  BANK  149 

119.  Borrowing  money.  If  the  time  comes  when  a  man 
wishes  to  start  in  business,  and  he  has  saved  some  money 
and  has  an  unquestionable  reputation  for  honesty,  he  will 
be  able  to  borrow  more  money  for  buying  a  business  or 
purchasing  goods.  Suppose  he  needs  $1000.  A  bank  will 
be  found  that  has  heard  enough  about  his  standing  to  lend 
him  the  money  if  he  has  a  good  indorser. 

120.  Indorser.  One  who  writes  his  name  across  the  back 
of  a  note  is  called  an  indorser.  The  indorser  is  responsible 
for  the  note  if  the  maker  does  not  pay  it.  * 

If  Richard  Roberts  will  indorse  for  John  Brown,  Mr.  Brown 
makes  out  a  note  like  this  : 


Boston-,  Mass.,  Tflay-  /6,  1^06 
Jw-o-   ryiantkoy  after  date,  u^CCkcyut   avoi^&,  c/  promise 
to  pay  to  the  order  of  f^i&kcivd  f^a^'&itoy    %fOOO.— 

at  Cbc  first  JVational  Sanh^  Boston,  J^Iass* 

Value  received 
Residence  7030  B&a.(^o-n  ^t.  fokn  Buyw-n 

Due  ^^it^f  16 


It  is  not  a  very  direct  way  of  borrowing  from  the  bank,  but 
it  is  a  common  one.  The  original  idea  was  that  Mr.  Brown 
borrowed  of  Mr.  Roberts,  and  Mr.  Roberts  sold  the  note  to  the 
bank,  thus  getting  the  money  to  lend  Mr.  Brown.  But  now  it 
means  simply  that  Mr.  Roberts  agrees  to  pay  if  Mr.  Brown  does 
not.    Banks  often  take  notes  payable  directly  to  the  cashier. 

Some  states  allow  three  "days  of  grace,"  that  is,  two  months 
means  two  months  +  three  days  ;  but  the  custom  is  rapidly  going 
out  of  use.    Teachers  should  use  them  where  it  is  the  custom. 


150  BANK  ACCOUNTS 

121.  Bank  discount.  The  note  described  on  page  149 
does  not  mention  interest.  This  is  because  the  borrower, 
Mr.  Brown,  pays  the  interest  to  the  bank  in  advance. 

Interest  paid  on  a  note  in  advance  is  called  hank  discount. 
The  note  is  then  said  to  be  discounted, 

122.  Illustrative  problem.  What  is  the  discount  on  the 
$1000  note  on  page  149  at  6%  a  year? 

The  discount  on  $1000  for  2  mo.  @  6%  a  year  is  $10. 
The  rate  of  discount  is  understood  to  be  by  the  year,  like  the 
rate  of  interest,  unless  the  contrary  is  stated. 

123.  Proceeds.  The  balance  after  deducting  the  discount 
from  the  face  of  a  note  is  called  the  proceeds. 

Thus,  the  proceeds  on  the  above  note  are  $1000  -  $10  =  $990. 

124.  Usual  time  for  bank  notes.  Notes  are  usually  made 
for  30,  60,  or  90  days,  and  are  then  renewed  if  desired. 

In  states  where  days  of  grace  are  allowed,  teachers  should  see  that 
they  are  included. 

ORAL   EXERCISE 

State  the  discount  on  the  following  : 
1.    $50,  2  mo.,  6%.  2.    $75,  2  mo.,  6%. 

3.    $125,  2  mo.,  6%.  4.    $650,  2  mo.,  6%. 

5.    $100,  1  mo.,  6%.  6.    $250,  1  mo.,  6%. 

7.    $400,  3  mo.,  6%.  8.    $600,  3  mo.,  6%. 

9.    $600,  2  mo.,  5%.  10.    $1200,  3  mo.,  6%. 

State  the  proceeds  on  the  following  notes^  discounted  as 
specified: 

11.    $100,  2  mo.,  6%.  12.    $300,  2  mo.,  6%. 

13.    $600,  1  mo.,  5%.  14.    $600,  3  mo.,  5%. 

15.    $1000,  3  mo.,  6%.  16.    $1000,  3  mo.,  5%. 


BANK  DISCOUNT  151 

WRITTEN    EXERCISE 

Find  the  discount  and  proceeds  on  the  following: 
1.    $875,  30  days,  6%.  2.    $975,  90  days,  5%. 

3.    $425,  30  days,  6%.  4.    $2568,  60  days,  5%. 

6.  $1250,  60  days,  6%.  6.    $1500,  90  days,  5%. 

7.  $2565,  90  days,  5%.  8.    $3250,  90  days,  5^%. 
9.    $4250,  30  days,  4^%.          10.    $325.50,  30 days,  6%. 

11.    $427.50,  60 days,  5%.  12.    $237.50,30  days,  5%. 

13.  Make  out  a  60-day  note  for  $750,  dated  to-day,  pay- 
able to  John  Doe's  order  at  some  bank  in  your  town  or 
city.    Discount  it  at  5%. 

14.  Make  out  a  30-day  note  for  $675,  dated  to-day,  pay- 
able to  Eichard  Roe's  order  at  some  bank  of  which  you 
know.    Discount  it  at  6%. 

15.  Make  out  a  90-day  note  for  $1250,  dated  to-day, 
payable  to  James  Jameson's  order  at  some  bank  of  which 
you  know.    Discount  it  at  6%. 

16.  A  man's  bank  account  shows  deposits,  $37.50,  $75, 
$82.50,  $100,  $50,  $300,  $40,  $125,  $500;  drawn  by  checks, 
$13.75,  %^2,  $5,  $125.50,  $82.75.  He  needs  $2000  to  start 
him  in  business,  and  wishes  to  keep  about  $500  in  the 
bank.    How  much  must  he  borrow,  to  the  nearest  $100? 

17.  If  he  makes  out  a  note  for  this  amount  for  90  days 
at  6%,  how  much  discount  must  he  pay?  What  are  the 
proceeds  ?    What  are  they  for  60  days  ? 

18.  A  merchant  has  to  pay  a  debt  of  $1275  less  10%. 
He  has  in  the  bank  $672.80,  and  has  $127.50  in  cash  in 
his  safe.  He  wishes  to  leave  about  $300  in  the  bank  and 
about  $Q5  in  his  safe.  How  much  must  he  borrow,  to  the 
nearest  $50?    Discount  the  note  for  30  days  at  6%. 


152  BANK  ACCOUNTS 

125.  Discounting  notes.  If  a  dealer  buys  some  goods  for 
the  fall  trade,  but  does  not  wish  to  pay  for  them  until 
after  the  holidays,  he  may  buy  them  on  credit,  giving  his 
note.  The  manufacturer  may  need  the  money  at  once,  in 
which  case  he  will  indorse  the  note  and  sell  it  to  a  bank 
for  the  sum  less  the  discount. 

126.  Illustrative  problem.  If  you  give  a  manufacturer  your 
note  dated  September  1,  due  on  January  1,  for  $500,  with 
interest  at  5%,  and  he,  needing  the  money,  discounts  it  at 
the  bank  on  September  16  at  6%,  what  are  the  proceeds? 

Face  of  the  note  =  $500. 

Interest  4  mo.,  5%  =  8.33 
Amount  at  maturity  =  $508.33 
Discount  107  da.,  6%  =  9.07 
Proceeds,  ^499.26 

Banks  usually  compute  the  discount  period  in  days.  In  some 
parts  of  the  country  both  the  first  and  last  days  are  included  in 
the  discount  period,  thus  making  it  108  days  in  the  above  exam- 
ple.   Teachers  should  be  guided  by  the  local  custom. 

ORAL  EXERCISE 

State  the  following  : 

1.  5%  of  $70.         2.  5%  of  $75.  3.    5%  of  $Q^. 

4.  4%  of  $m.         5.  4%  of  $35.  6.   4%  of  $95. 

7.  6%  of  $75.         8.  6%  of  %%6,  9.    6%  of  $65, 

10.  3%  of  $125.    11.  3%  of  $225.       12.    3%  of  $365. 

13.  2%  of  $42.50.  14.    2%  of  $63.50. 

15.  2%  of  $27.50.  16.    4%  of  $20.25. 

17.  4%  of  $15.25.  18.    4%  of  $41.25. 

19.  5%  of  $15.20.  20.    5%  of  $20.40. 

21.  5%  of  $30.60.  22.    6%  of  $25.50. 


DISCOUNTING  NOTES 


153 


WRITTEN  EXERCISE 


Find  the  discount  and  proceeds : 


Face 

Date 

Due 

Interest 

Date  of 
Discount 

Rate  oj 
Discoun 

1. 

$300 

July  1 

July  31 

4% 

July  16 

6%. 

2. 

$800 

Sept.  1 

Nov.  1 

5% 

Sept.  11 

6%. 

3. 

$550 

Oct.  1 

Jan.  1 

4% 

Dec.  2 

6%. 

4. 

$325 

July  1 

Dec.  1 

6% 

Nov.  1 

5%- 

5. 

$1000 

Nov.  1 

Dec.  1 

6% 

Nov.  1 

6%. 

6. 

$1250 

Aug.  15 

Jan.  1 

5% 

Sept.  1 

5%. 

Exs.  7-32  draw  no  interest. 

7.  $3750,  60  days,  5%. 

9.  $9500,  63  days,  6%. 

11.  $4225,  93  days,  5%. 

13.  $7500,  33  days,  5%. 

15.  $42.50,  30  days,  6%. 

17.  $35.50,  30  days,  6%. 

19.  $125.50, 60  days,  6%. 

21.  $375.50,  90  days,  6%. 

23.  $457.50,  30 days,  5%. 

25.  $287.60,  90  days,  5%. 

27.  $2750,  93  days,  4^%. 

29.  $4760,  63  days,  5^%. 

31.  $1545,  33  days,  4^%. 


8.  $4225,  60  days,  5%. 

10.  $7500,  63  days,  5%. 

12.  $5575,  93  days,  6%. 

14.  $4750,  33  days,  6%. 

16.  $27.60,  30  days,  6%. 

18.  $28.75,  30  days,  6%. 

20.  $275.25,  60  days,  6%. 

22.  $450.75,  90  days,  6%. 

24.  $296.50,  30  days,  5%. 

26.  $375.40,  90  days,  5%. 

28.  $3275,  93  days,  4^%. 

30.  $2745,  63  days,  5^%. 

32.  $1575,  33  days,  3J%. 


33.  The  discount  on  a  note  for  90  days  at  6%  is  $18.75. 
What  is  the  face  of  the  note  that  is  discounted  ? 

34.  A  dealer  buys  $1750  worth  of  goods,  giving  his  note 
on  October  4,  for  90  days,  at  5%.  On  October  10  the  holder 
of  the  note  discounts  it  at  6%.    Find  the  proceeds. 


154  PARTIAL  PAYMENTS 


PARTIAL  PAYMENTS 


127.  Partial  payments.  If  a  dealer  holds  a  note  against 
one  of  his  customers,  and  it  bears  interest,  and  partial  pay- 
ments are  made  from  time  to  time,  the  amount  due  on  the 
day  of  settlement  is  found  in  the  following  way: 

1.  Add  the  interest  to  the  principal  whenever  the  payment 
(or  sum  of  the  payments)  equals  or  exceeds  the  interest. 

2.  Then  deduct  the  payment  {or  payments)  and  continue 
as  before. 

This  is  the  United  States  Rule  of  Partial  Payments^  the  legal  one 
in  most  states.  Where  other  rules  are  legal,  teachers  should  explain 
the  law  and  require  the  problems  solved  accordingly. 

128.  Illustrative  problem.  A  note  for  $1000,  at  5%,  is 
dated  January  1,  1906.  The  following  payments  are  in- 
dorsed (written  across  the  back,  as  is  the  custom)  :  July  1, 
1906,  $10;  January  1,  1907,  $40;  July  1,  1907,  $20; 
January  1,  1908,  $130.    How  much  is  due  July  1,  1908? 

The  interest  on  July  1,  1906,  is  ^25,  and  the  payment  is  |10. 
Hence  the  payment  cannot  be  deducted.  The  reason  is  easily 
seen,  for  if  we  should  take  $1025  -  $10  =  $1015  as  the  new  prin- 
cipal, we  should  be  drawing  interest  on  more  than  the  $1000. 

First  principal,  .  *  $1000 

Int.  for  1  yr.,  50 

First  amount,  January  1,  1907,  $1050 

1st  and  2d  payments,  50 

Second  principal,  January  1,  1907,  $1000 

Int.  for  1  yr.,  50 

Second  amount,  January  1,  1908,  $1050 

3d  and  4th  payments,  150 

Third  principal,  $900 

Int.  for  6  mo.,  22.50 

Due  July  1,  1908,  $922.50 


UNITED  STATES  RULE  165 

WRITTEN  EXERCISE 

1.  A  note  for  $375,  at  5%,  has  a  payment  of  $18.75 
indorsed  annually  at  the  close  of  each  year  from  its  date, 
for  3  years.  How  much  is  due  at  the  end  of  the  fourth  year  ? 

2.  A  note  for  $500,  at  6%,  is  dated  January  1,  1906, 
and  has  the  following  partial  payments  indorsed :  July  2, 
1906,  $100 ;  January  1,  1907,  $100.  How  much  is  due 
July  1,  1907? 

3.  A  note  for  $300,  at  6%,  is  dated  April  1,  1906,  and 
has  the  following  partial  payments  indorsed  :  September  1, 

1906,  $50;  February  16,  1907,  $75 ;  January  1,  1908,  $100. 
How  much  is  due  July  1,  1908  ? 

4.  A  note  for  $1800,  at  5%,  is  dated  April  16, 1906,  and 
has  the  following  partial  payments  indorsed:  July  2, 1906, 
$500;  October  1,  1906,  $250;  February  1,  1907,  $100; 
May  1,  1907,  $375.  How  much  is  due  September  5,  1907? 

5.  A  note  for  $750,  at  4%,  is  dated  June  15,  1906,  and 
has  the  following  partial  payments  indorsed :   March  6, 

1907,  $200;  September  6,  1907,  $150;  January  17,  1908, 
$250.  How  much  is  due  on  the  day  of  settlement,  May  14, 
1908? 

6.  A  note  for  $600,  at  5%,  is  dated  July  2,  1906,  and 
has  the  following  partial  payments  indorsed :  January  2, 
1907,  $50;  February  11,  1907,  $75;  July  8,  1907,  $200; 
September  10,  1907,  $80  ;  November  2,  1907,  $50.  How 
much  is  due  January  2,  1908? 

7.  A  note  for  $1200,  at  4%,  is  dated  May  1,  1906,  and 
has  the  following  partial  payments  indorsed :  July  2, 1906, 
by  labor,  $5  ;  July  9, 1906,  by  labor,  $2;  September  1, 1906, 
$93 ;  May  1,  1907,  $450 ;  November  1,  1907,  $500.  How 
much  is  due  January  1,  1908? 


156  PARTIAL  PAYMENTS 

8.  A  note  for  $750,  at  6%,  is  dated  February  2,  1907, 
and  has  the  following  partial  payments  indorsed :  June  2, 
1907,  $150 ;  July  17, 1907,  $75 ;  February  2,  1908,  $100. 
How  much  is  due  August  2,  1908  ? 

9.  A  note  for  $575,  at  6%,  is  dated  January  15,  1906, 
and  has  the  following  partial  payments  indorsed :  May  7, 

1906,  $30  ;  August  13,  1906,  $50  ;  December  18, 1906,  $75. 
How  much  is  due  January  30,  1907? 

10.  A  note  for  $625,  at  5%,  is  dated  November  13, 1906, 
and  has  the  following  partial  payments  indorsed ;  Febru- 
ary 14,  1907,  $35 ;  April  17,  1907,   $75.50 ;  October  23, 

1907,  $50 ;  March  19,  1908,  $135.    How  much  is  due  Sep- 
tember 23,  1908  ? 

11.  A  note  for  $175,  at  6%,  is  dated  December  9,  1907, 
and  has  the  following  partial  payments  indorsed :  Febru- 
ary 4,  1908,  $25;  May  27,  1908,  $63.50;  September  2, 

1908,  $15;  February  25,  1909,  $20.    How  much  is  due 
April  22,  1909  ? 

12.  A  note  for  $675.50,  at  5%,  is  dated  August  5, 1907, 
and  has  the  following  partial  payments  indorsed  :  January 
7,  1908,  $50;  August  5,  1908,  $50;  March  18,  1909,  $35; 
July  15, 1909,  $75  ;  November  11, 1909,  $130.  How  much 
is  due  January  7,  1910  ? 

13.  A  man  owes  another  $750  for  a  village  building  lot, 
and  he  gives  his  note  at  6%,  due  on  demand,  with  the 
understanding  that  he  should  pay  part  of  it  by  labor.  The 
note  is  dated  April  15, 1908,  and  the  following  partial  pay- 
ments are  indorsed :  July  22,  1908,  4  days'  labor  @  $3 ; 
September  16, 1908,  3^  days'  labor  @  $3  ;  January  21, 1909, 
4 J  hours'  labor  @  50/;  March  11,  1909,  11 J  days'  labor  @ 
$3 ;  July  15,  1909,  37  days'  labor  @   $3  ;  September  16, 

1909,  cash,  $350.    How  much  is  due  January  1,  1910? 


MERCHANTS'  RULE  157 

129.  Merchants'  rule.  Where  a  note  or  account  runs  a  year 
or  less,  and  partial  payments  have  been  made,  business  men 
often  compute  the  balance  due  by  means  of  a  rule  some- 
times called  The  Merchants'  Rule,  as  follows : 

1.  Find  the  amount  of  the  principal  at  the  time  of  settle- 
ment, 

2.  Find  the  amount  of  each  payment  from  the  time  it  was 
made  until  the  time  of  settlement. 

3.  From  the  amount  of  the  principal  subtract  the  amount 
of  the  payments. 

The  rule,  not  being  as  fair  for  longer  periods  as  the  United 
States  Rule,  is  not  legal.  But  for  short  periods  it  is  easier  and 
gives  nearly  the  same  result. 

130.  Illustrative  problem.  A  note  for  $100  made  January  1 
has  the  following  payments  indorsed :  March  1,  $10 ; 
April  1,  $25.  Find  the  balance  July  1,  allowing  6%  interest. 

Amount  of  #100  for  6  mo.  $103 

a  u     $10    u    4    "    $10.20 

«  "     $25    ''    3    ''      25.38 

35.58 
Balance,  $67.42 

WRITTEN  EXERCISE 

Notes  for  the  following  amounts  have  indorsed  the  pay- 
ments indicated.  Find  the  balance  at  the  date  of  settle- 
ment^ using  the  Merchants^  rule^  and  allowing  6%  interest: 

1.  $875,  April  1.  Indorsements:  $300,  May  1;  $125, 
June  15 ;  $275,  July  25.     Settled  November  20. 

2.  $250,  February  1.  Indorsements :  $30,  March  1  ; 
$70,  May  15  ;    $50,  July  10.     Settled  September  15. 

3.  $750,  March  1.  Indorsements:  May  10,  $100; 
July  12,  $75  ;  September  4,  $40.     Settled  October  15. 


158  TRADE  DISCOUNT 

TRADE  DISCOUNT 

131.  Advantage  of  trade  discount.  Dealers  wish  to  buy 
their  goods  at  as  great  a  discount  as  possible.  When  they 
pay  cash  for  them  they  get  the  best  price,  because  a  special 
discount  is  usually  allowed  for  cash. 

132.  Several  discounts.  We  have  already  met  cases  in 
this  series  of  arithmetics  in  which  more  than  one  discount 
was  allowed.  Sometimes  more  than  two  are  allowed,  new 
discount  lists  being  sent  to  retail  dealers  as  the  cost  of 
production  changes. 

ORAL    EXERCISE 

1.  What  is  the  cost  of  goods  listed  at  $300,  5%  off  ? 

2.  What  is  the  cost  of  goods  listed  at  $600,  at  ^  off  ? 

3.  What  is  the  cost  of  goods  listed  at  $250,  10%  off? 

4.  If  on  a  bill  of  goods  amounting  to  $250  a  discount  of 
20%,  10%  is  allowed,  what  is  the  net  price  ? 

$250  -  150  =  $200  ;    $200  -  $20  =  $180. 

State  the  cost  of  goods  listed  as  follows^  less  the  discount : 

5.  $250,  10%,  4%.  6.  $200,  5%,  1%. 

7.  $300,10%,!%.  8.  $250,  20%,  4%. 

9.  $100,  10%,  10%.  10.  $500,  20%,  6%. 

11.  $200,  15%,  10%.  12.  $400,  25%,  10%. 

13.  $1250,  20%,  3%.  14.  $660,  33J%,  5%. 

15.  $400,  12i%,  2%.  16.  $1000,  15%,  2%. 

17.  $300,  33^%,  10%.  18.  $600,  33J%,  10%. 

19.  $600,  16§%,  10%.  20.  $500,  20%,  12i%. 

21.  $1000, 10%,  10%.  22.  $540,  16f %,  10%. 


PRICE  LISTS  159 

133.  Sample  price  list.  The  following  is  a  price  list  of 
certain  school  supplies,  with  the  discounts  allowed  to  schools 
and  dealers  where  the  prices  are  not  net : 


Rulers, 

$0.35 

pel 

'  doz.,  net 

Composition  books, 

4.50 

(( 

gross,  less  5% 

Thumb  tacks, 

0.40 

a 

100,       "    40% 

Drawing  pencils. 

4.71 

ii 

gross,     "    20% 

Drawing  paper  9  X  12, 

,  1.10 

li 

package,  less  jV 

Pens, 

0.61 

" 

gross,  less  J,  10% 

Tubes  of  paste, 

4.05 

" 

''        ^'    10%,  5% 

Penholders, 

3.20 

a 

"    12%,  5% 

Drawing  compasses. 

1.65 

ii 

doz.,       *'    10%,  5% 

WRITTEN  EXERCISE 

1.  How  much  must  your  school  pay  for  ^  gross  of  pen- 
holders? for  i  gross?  for  a  gross? 

2.  The  school  wishes  to  buy  5  packages  of  drawing  paper 
and  300  thumb  tacks.    What  will  they  cost? 

3.  What  will  8  gross  of  pens  and  ^  gross  of  composition 
books  cost  ?  2  gross  of  pens  and  1  doz.  rulers  ? 

4.  There  are  40  pupils  in  a  class,  and  each  needs  draw- 
ing compasses  and  a  ruler.  What  will  they  cost  the  school  ? 
Suppose  there  were  60  pupils  ? 

5.  If  a  dealer  sells  pens  at  a  cent  apiece,  what  does 
he  gain  per  gross  ?  If  he  sells  penholders  at  2  ct.  each, 
what  does  he  gain  per  gross  ? 

6.  A  dealer  buys  a  gross  of  rulers  and  a  gross  of  drawing 
pencils.  He  sells  both  at  5  ct.  each.  What  does  he  gain 
on  the  lot  ?    Suppose  he  buys  2  gross  of  each  ? 

7.  If  a  dealer  buys  a  gross  of  tubes  of  paste  for  mount- 
ing pictures,  and  sells  the  tubes  at  5  ct.  each,  what  does 
he  gain  on  the  purchase?    How  much  on  3  gross? 


160  TRADE  DISCOUNT 

134.  Ordering  goods.    The  following  is  a  model  order  : 

WOOD    &    ROBERTS 

BOOKSELLERS 

Memphis,  Tenn.,   Feb.  15.   19  07 

Messrs.  Ginn  &  Company,  Publishers, 

378  Wabash  Ave..  Chicago,  111. 
Dear  Sirs:  Please  send  at  once,  by  express. 

75  Smith's  Practical  Arithmetics. 
60   '*    Primary  Arithmetics. 

Yours  truly. 

WOOD  &  ROBERTS 

135.  Model   bill.    The  following  is  the  bill  that  Ginn 
&  Company  would  send  in  reply: 

Messrs.  Wood  &  Roberts. 

Memphis,  Tenn.  Feb.  16.   19  07 

Bought  of  GINN    &    COMPANY 

Educational   Publishers 
378    WABASH    AVE..   CHICAGO 
Terms  of  this  Invoice:  Net  Cash 

75  Smith's    Practical  Arithmetics.  $.65     $48.75 

60        **  Primary  Arithmetics.  .35       21.00 

$69.75 
1/6    11.62 

$58.13 

It  is  customary  to  state  per  cents  like  16f%,  12  J%,  20%,  and  25% 
in  the  common-fraction  form,  as  above. 


BILLS  OF  GOODS  161 

WRITTEN  EXERCISE 

Write  both  orders  and  hills  for  the  following  goods 
bought  of  yourself  by  the  person  named  or  by  some  one 
you  know: 

1.  Bought  2  doz.  tennis  rackets  @  $21 ;  8  doz.  balls  @ 
$3;  f  doz.  tennis  nets  @  $19.20.    Discount  12%,  5%,  2%. 

2.  Henry  James,  Des  Moines,  Iowa :  \  doz.  rugs  @  $84 ; 
750  yd.  carpet  @  82/;  3  doz.  hassocks  @  $6.    Discount  \, 

3.  Bought  12  doz.  tumblers  @  $1.05 ;  35  doz.  dinner 
plates  @  $2.50  ;  IJ  doz.  sugar  bowls  @  $9.60.    Discount  i. 

4.  Jones  &  Co.,  3497  Wabash  Ave.,  Chicago :  2  bbl.P.R. 
molasses  @  $12 ;  200  lb.  Eio  tapioca  @  6  ct. ;  150  lb.  Mocha 
coffee  @  20  ct.    Discount  6%. 

5.  Bought  5  doz.  bottles  of  ink  @  $3 ;  300  lb.  paper  @ 
30  ct. ;  2  doz.  bottles  of  mucilage  @  $4 ;  6  gross  pencils 
@  $2.75.    Discount  3%,  2%,  1%. 

6.  George  Lloyd,  Lincoln,  Neb. :  18  brass  bedsteads, 
No.  142,  @  $17.25 ;  15  woven  wire  mattresses,  No.  16,  @ 
$3.45;  3  sideboards,  No.  196,  @  $17.25.    Discount  i. 

7.  Newton  &  Co.,  2831  Spring  St.,  New  York  :  21  Ohio 
steers,  1226  lb.  (average),  @  $5.10  (per  100  lb.)  ;  20  do. 
(ditto  =  the  same),  1247  lb.,  @  $5.10 ;  20  do.,  1112  lb.,  @ 
$4.95.    Discount  yL. 

8.  Sherman  &  Culver,  New  York :  20  Illinois  steers, 
1157  lb.  (see  Ex.  7),  @  $4.60.;  28  do.,  996  lb.,  @  $4.12|.; 
20  Kentucky  steers,  1230  lb.,  @  $4.80 ;  7  Indiana  do., 
1078  lb.,  @  $4.70.    Discount  ^^, 

9.  E.  B.  Homer,  Buffalo :  75  180-lb.  bags  of  Western 
potatoes  @  $1.48;  50  150-lb.  do.  @  $1.28;  125  168-lb.  do.  @ 
$1.42 ;  1620  lb.  Jersey  potatoes  in  bulk  @  $1.47  per  180  lb. 
Discount  J. 


162 


SIMPLE  ACCOUNTS 


SIMPLE  ACCOUNTS 

136.  The  debit  column.  In  his  account  a  man  charges  his 
income  to  himself,  and  places  it  in  the  left  column.  He 
is  debtor  {Dr.)  to  himself  for  this  column. 

137.  The  credit  column.  His  expenditures  he  credits  to 
his  account,  and  places  them  in  the  column  marked  Cr, 


19 

Cash  on  hand 

Carfare  .10,  pencil  .06 

Drawing  book  .15,  ink  .10 

Geography 

Paper  .10,  ruler  .05 

Balance 

Dr. 

Cr. 

Jan.    7 
"      7 
«      8 
"      9 
"    12 
«    14 

7 

7 

45 
45 

1 

5 

7 

15 

25 
12 
15 
78 
45 

WRITTEN   EXERCISE 

1.  Make  out  the  following  account  for  a  day.  Cash  on 
hand,  $174.30;  Eeceipts,mdse.,  $12.50,  $6.75,  $0.42,  $17.30, 
$9.50,  $42.75;  Expenses,  Perry  &  Co.  bill,  $75.82. 

2.  Make  out  the  following  account  for  a  week.    Cash  on 
hand,  $21.30;    Peceipts,  from  apples  sold,   $7.50;    Eggs, 
$3.25;  Poultry,  $6.90.    Disbursements, Horseshoeing,  $0.75;^ 
Eepairs  to  wagon,  $1.20;  Shingles,  $4.20;  Seed,  $3.50. 

3.  Make  out  the  following  account  for  a  week.  Cash  on 
hand,  $1.75;  Receipts,  weekly  allowance,  $1.  Expenses, 
Writing  paper,  10  ct. ;  Pencils,  8  ct. ;  Ink,  10  ct. ;  Compasses, 
10  ct. ;  Arithmetic,  90  ct. ;  Penholder,  3  ct. ;  Eraser,  5  ct. 

Pupils  should  be  required  to  make  out  imaginary  accounts. 


ACCOUNTS  163 

Make  out  the  following  accounts  for  last  iveeJc^  inserting 
the  proper  year^  months  and  day  of  the  month : 

4.  Dr.,  Monday,  Cash  on  hand,  $1.05 ;  Allowance  for 
house  expenses,  $6;  Thursday,  Sewing  for  Mrs.  Graham, 
$1.  Or.,  Tuesday,  Groceries,  $1.35;  Meat,  85/;  Wednes- 
day, Meat,  $1.08 ;  Thursday,  Groceries,  $2.30 ;  Saturday, 
Meat,  $1.12. 

5.  Dr.,  Monday,  Cash  on  hand,  $17.50;  Eggs  sold, 
$4.20;  Tuesday,  Corn  sold,  $26.50;  Poultry  sold,  $6.75; 
Thursday,  3  T.  750  lb.  hay  sold  @  $8.  Cr.,  Tuesday,  4  days' 
wages,  John  Cobb,  @  $2.50;  Wednesday,  Grocery  bill, 
$7.28;  Friday,  Eepairs,  $1.60. 

6.  Dr.,  Monday,  Cash  on  hand,  $26.70 ;  Saturday, Wages, 
$15.  Cr.,  Monday,  Allowance  for  house,  $7.50 ;  Carfare, 
10/;  Tuesday,  Carfare,  10/;  Wednesday,  Eent,  $20;  Car- 
fare, 10/;  Thursday,  Carfare,  10^;  Friday,  Shoes,  $3; 
Saturday,  Suit  for  Eob,  $6.40. 

7.  Dr.,  Monday,  Cash  on  hand,  $9.75;  Allowance  for 
house  expenses,  $10;  Thursday,  Sale  of  old  suit,  $1.25. 
Cr.,  Tuesday,  Meat  bill,  95/;  Carfare,  15/;  Grocer,  $1.68 ; 
Wednesday,  Meat  bill,  $1.30;  Grocer,  $2.15;  Thursday, 
Laundry,  60/;  Gas  bill,  $1.80;  Friday,  Ice,  $1.60; 
Grocer,  $3.60;  Meat  bill,  $1.42;  Broom  and  ironing 
board,  $1.10. 

8.  Dr.,  Monday,  Cash  on  hand,  $278.50;  Sales,  $72.80; 
Tuesday,  Sales,  $98.75;  Wednesday,  Sales,  $126.40; 
Sale  of  old  show  case,  $6.50 ;  Thursday,  Sales,  $82.75  ; 
Friday,  Sales,  $110.62 ;  Saturday,  Sales,  $96.30.  Cr., 
Monday,  Gorham  bill,  $168.40  less  10%;  Tuesday, 
Whiting  bill,  $68.90  net;  Barton  bill,  $137.50  less  6%; 
Saturday,  Frank's  wages,  $12.50;  Morgan's  wages,  $15; 
Hulbert's  wages,  $14. 


164  PARTNERSHIP 


PARTNERSHIP 


138.  Partitive  proportion.  If  partners  invest  equal  sums  and 
contribute  equally  in  work,  the  profits  are  divided  equally. 
Otherwise  partitive  proportion  (page  119)  is  employed. 

139.  Partners  usually  have  an  annual  settlement.  Money 
withdrawn  by  any  partner  during  the  year  is  charged  to  him 
with  interest  at  the  settlement. 

140.  Illustrative  problem.  Brown,  Edgcomb,  and  Thomas 
form  a  partnership  on  February  1,  Brown  putting  in  $2500, 
Edgcomb  $4000,  and  Thomas  $3500.  "What  is  the  share 
of  each  in  $6000  profits  on  the  following  February  1  ? 

1.  Since  the  total  capital  is  $10,000,  and  Brown  put  in  $2500, 

Brown's  share  is  tVoVo?  ^^  /o? 
Edgcomb's  "  "  j%%%%  "  ^0, 
Thomas's    ''     *'  ^oVo%  ''  2V 

2.  Therefore  Brown  receives  /^  of  $6000,  or  $1500 


Edgcomb 
Thomas 
The  total 

a 

being 

1 

"        "       "  $2400 

'^         "       "  $2100 

$6000 

ORAL    EXERCISE 

Separate  into  two  parts  having  the  given  ratio : 

1.    $150,  1 :  2. 

2.    $500,  2  :  3. 

3.    $400,  3  : 1. 

4.    $500,  1  :  3. 

5.    $250,  2  :  3. 

6.    $350,  3  :  4. 

7.    $180,4:5. 

8.    $330,  4  :  7. 

9.    $560,3:5. 

10.    $660,  8  :  3. 

11.    140  ft.,  5  :  9. 

12.    132  yd.,  7:5. 

13.    600  ft.,  8  :  7. 

14.    450  yd.,  7  :  8. 

15.    420  rd.,  10  :  11. 

16.    260  mi.,  11 :  15. 

PARTNERSHIP  165 

WRITTEN  EXERCISE 

1.  X,  Y,  and  Z  invest  $345,  $625,  and  $730,  respectively. 
They  make  $153.    What  is  the  share  of  each? 

2.  A,  B,  and  C  invest  $2200,  $3350,  and  $1650,  respec- 
tively.   They  make  $1440.    What  is  the  share  of  each? 

3.  Eoberts,  Jacobs,  and  Jameson  invest  $2700,  $3250, 
and  $2050,  respectively.  They  make  $2400.  What  is  the 
share  of  each? 

4.  A,  B,  and  C  pay  $195  irrigation  taxes  for  their 
farms.  A  has  250  acres,  B  180  acres,  C  220  acres.  What 
is  the  share  of  each  ? 

5.  X,  Y,  and  Z  pay  $1085  for  some  water  power.  X 
uses  30  horse  power,  Y  45  horse  power,  Z  80  horse  power. 
What  should  each  pay? 

6.  Three  men  rent  a  summer  cottage.  The  first  occupies 
it  5  weeks,  the  second  4  weeks,  and  the  third  3  weeks. 
At  $264  for  the  season,  what  should  each  pay? 

7.  Day  and  McFarlane  pasture  some  cattle  in  a  field, 
Day  putting  in  62  head  for  7  weeks,  and  McFarlane  48 
head  for  5  weeks.  The  bill  for  pasturage  being  $101.10, 
how  much  should  each  pay? 

8.  Two  contractors  for  rock  excavating  in  a  tunnel  run 
16  and  21  drills  respectively,  getting  compressed  air  from 
the  same  engine.  If  the  expense  of  furnishing  the  com- 
pressed air  is  $555,  what  is  the  share  of  each? 

9.  Two  farmers  whose  lands  join  have  a  windmill  and 
tank  in  common.  They  pay  for  the  annual  repairs  accord- 
ing to  the  greatest  number  of  head  of  cattle  kept  by  each 
at  any  time  during  the  year.  If  they  have  37  and  48  head 
respectively,  and  the  repairs  amount  to  $25.50,  what  is 
the  share  of  each? 


166  PARTNERSHIP 

10.  Messrs.  Brown  and  Jones  form  a  partnership,  Brown 
furnishing  $4200  and  Jones  furnishing  $3300.  After  a 
year  Brown  puts  in  $500  more.  At  the  end  of  2  years 
they  sell  out  for  $9300.    How  much  should  each  receive  ? 

11.  Ayres  and  Ives  go  into  partnership,  Ayres  putting 
in  $3500  and  Ives  $6500.  Ives  is  to  give  all  of  his  time 
to  the  business  and  take  out  $2000  before  any  division 
of  profits.  If  they  make  $2500  this  year,  to  how  much  of 
it  is  each  entitled? 

12.  Glover  and  Staughton  go  into  partnership,  Staugh- 
ton  putting  in  $7000  and  Glover  $9000.  Glover  doing 
no  work,  it  is  agreed  that  Staughton  shall  take  $2000 
a  year  from  the  profits  before  a  division.  The  profits  last 
year  were  $6400.    What  was  the  share  of  each  ? 

13.  Webb,  Bull,  and  Smith  form  a  partnership,  Webb 
putting  in  $8000,  Bull  $3000,  and  Smith  $5000.  It  is 
agreed  that  Bull  shall  contribute  no  work,  but  that  Webb 
shall  receive  $1500  and  Smith  $900  before  the  rest  of  the 
profits  are  divided.  The  year's  profits  were  $7200.  How 
much  did  each  receive? 

14.  Messrs.  Davids,  Glover,  and  James  buy  a  house  for 
$9500.  Davids  puts  in  $3200,  and  Glover  and  James  put 
in  the  rest.  Glover  putting  in  half  as  much  as  James. 
They  rent  the  house  this  year  for  10%  of  its  cost,  and  pay 
$15  for  insurance,  $40  for  taxes,  and  $40  for  repairs. 
What  is  the  share  of  each  in  the  net  receipts? 

15.  Wood,  Wallace,  and  Harris  own  a  spring,  and  pay 
for  repairs  to  the  spring  house  and  piping  according  to  the 
amount  of  water  used  by  each,  as  shown  by  their  water 
meters.  If  the  respective  amounts  used  during  a  given 
period  are  34,000  gal.,  26,500  gal.,  and  42,500  gal.,  what  is 
the  share  of  each  in  repairs  amounting  to  $24.72  ? 


EXCHANGE  167 

EXCHANGE 

141.  Paying  bills  at  a  distance.  If  a  man  owes  money  to 
some  one  living  in  another  place,  lie  may  send  it  by  a 
registered  letter.  He  will  be  more  likely,  however,  to  pay 
his  bill  by  a  check,  a  money  order,  or  a  draft. 

142.  Exchange.  The  payment  of  money  by  means  of 
checks,  money  orders,  or  drafts  is  called  exchange, 

143.  Paying  by  check.  If  a  man  sends  his  check  for  the 
amount,  the  one  to  whom  he  owes  the  money  will  deposit 
it  in  the  bank  where  he  keeps  his  account.  This  bank 
will  send  it  to  the  debtor's  bank  for  collection,  and  will 
probably  charge  a  small  amount  for  the  trouble. 

144.  Paying  by  money  order.  A  money  order  may  be  pur- 
chased at  the  post  office,  or  from  an  express  company^  or  it 
may,  at  considerable  expense,  be  telegraphed.  Postal  or 
express  orders  may  be  sent  to  the  creditor,  who  can  then 
obtain  the  money  at  his  post  or  express  office.  The  extra 
cost  of  postal  money  orders  is  as  follows  : 

For  sums  not  exceeding  $2.50,  3  cents ;  above  this,  not  exceed- 
ing, $5,  5  cents;  above  this,  not  exceeding  $10,  8  cents;  above 
this,  not  exceeding  $20,  10  cents;  above  this,  not  exceeding  $30, 
12  cents;  above  this,  not  exceeding  $40,  15  cents;  above  this, 
not  exceeding  $50,  18  cents  ;  above  this,  not  exceeding  $60,  20 
cents;  above  this,  not  exceeding  $75,  25  cents;  above  this,  not 
exceeding  $100,  30  cents. 

ORAL  EXERCISE 

Referring  to  the  above  list^  state  the  cost  of  money 
orders  for  : 

1.    $31.50.  2.    $52.75.         3.    $92.30.         4.    $16.30. 

5.    $19.90.  6.    $86.50.         7.    $69.95.         8.    $90-50. 


168  EXCHANGE 

145.  Paying  by  bank  draft.  One  of  the  most  common 
methods  of  paying  a  debt  in  another  place,  particularly 
debts  of  large  size,  is  by  means  of  the  bank  draft. 


No.  ^8/0^ 
MERCHANTS  NATIONAL  BANK  OF  AUSTIN 

Austin,  Texas,  ^ulof  6,   1^07 

Pay  to  the  order  of fo-hyv  Ro-{>-&vU $78 J-^ 

^eA}-e.7iXAf-&Ufkt  CL'yvcL  ^ Dollars 

Co  Che  Chemical  I^ational  Bank,  ^'    ^^'    ^^^^ 

l^ew  -^ork  City  Cashier 


A  draft  is  therefore  the  same  as  a  check,  except  that  it  is  made 
by  the  cashier  of  some  bank  and  is  drawn  on  another  bank. 

Banks  usually  charge  a  slight  premium  on  the  face  of  the  draft. 
Thus,  a  $250  draft  at  0.1%  premium  would  cost  $250  +  0.1%  of 
$250  =  8250.25. 

If  John  Roberts,  who  purchased  the  above  draft,  owed  Robert 
Jones  the  money,  he  would  indorse  it,  thus : 

c9a^Y  to  tk&  avcC&v  o-i  Ro^eAZ  jcyyi&Qy 

It  might  also  have  been  made  payable  directly  to  the  order  of 
Robert  Jones  in  the  first  place,  but  this  is  not  the  custom. 

Drafts  on  large  money  centers  are  usually  cashed  for  customers 
of  the  bank  without  any  discount. 

146.  Illustrative  problem.  What  would  the  above  draft 
cost  at  0.1%   premium? 

0.1%  of  $78.75  =  $0.08,  to  the  nearest  cent. 
The  bank,  however,  would  probably  charge  \^f  to  make  a  con- 
venient amount.    Therefore  it  would  cost  $78.85. 


BANK  DRAFTS  169 

WRITTEN  EXERCISE 

1.  What  will  a  draft  for  $300  cost  at  ^%  premium? 

2.  What  will  a  draft  for  $3200  cost  at  0.1%  premium? 
for  $2500  at  ^^^  premium? 

3.  What  will  a  postal  money  order  for  $37.50  cost?  for 
$62.75?  for  $14.30?  for  $86.50?  for  $75.40? 

4.  What  will  a  New  Orleans  merchant  pay  for  a  draft 
on  Chicago  for  $2750  at  40/  premium  per  $1000? 

5.  When  the  government  charges  30/  per  $100  for  a 
money  order,  what  per  cent  premium  does  it  charge  ? 

6.  A  draft  cost  a  merchant  $2752.75,  including  0.1% 
premium.  What  was  the  face  of  the  draft?  What  was 
the  premium  ?    Write  the  draft. 

7.  A  draft  cost  a  merchant  $3751.50,  including  the 
premium  of  40/  per  $1000.  What  was  the  face  of  the 
draft  ?     What  was  the  premium  ? 

8.  If  a  man  owes  to  different  jobbers  from  whom  he 
buys  goods  $250,  $150,  $100,  and  $350,  what  will  drafts 
for  these  amounts  cost  at  0.1%  premium? 

9.  Which  is  cheaper  for  you,  if  you  owe  $75  for  some 
goods,  to  send  a  money  order,  or  a  draft  for  which  you 
have  to  pay  15/  premium  ?    How  much  cheaper  ? 

10.  It  costs  8/,  besides  postage,  to  register  a  letter.  If 
it  is  not  delivered  the  government  will  pay  the  loss,  up  to 
$25.  If  you  owe  $18,  is  it  cheaper  for  you  to  send  it  by 
registered  letter  or  by  money  order?    How  much  cheaper? 

11.  If  you  owe  $100  to  a  manufacturer  at  a  distance, 
from  whom  you  have  bought  goods,  how  will  you  make  the 
payment?  Tell  why  you  will  make  it  in  that  way,  and  how 
much  it  will  probably  cost.  (The  premium  on  drafts  may 
be  taken  at  the  common  rate  of  0.1%.) 


170  EXCHANGE 

147.  Commercial    drafts.     A    creditor    sometimes    draws 
directly  on  a  debtor,  the  draft  being  of  this  form  : 


Daytoist, 

Ohio,   Se^. 

16,  19/^ 

At  sight  pay  to  the  order  of 

%7S6.so_ 
—  Dollars 

148.  Parties  to  a  draft.  Here  the  National  Cash  Eegister 
Company  is  the  drawer;  Wye  is  the  drawee;  The  First 
National  Bank  is  the  payee. 

149.  The  Register  Company  deposits  this  draft  with  the  First 
National  Bank.  The  bank  sends  it  to  some  bank  in  Cleveland. 
The  Cleveland  bank  sends  a  messenger  to  Mr.  Wye  for  the  money, 
and,  having  collected  it,  sends  the  money  (or  its  equivalent)  to 
the  Dayton  bank.  The  Dayton  bank  th6n  notifies  the  company 
that  it  is  paid,  and  the  amount,  less  some  slight  commission, 
the  proceeds  of  the  draft,  is  added  to  the  company's  account. 

WRITTEN  EXERCISE 

1.  Brown  &  Co.  draw  on  J.  H.  Brownson  for  $750.  The 
banks  charge  0.1%  for  collection.    What  are  the  proceeds? 

2.  The  Electric  Company  draws  on  Mr.  X  for  $550.  The 
banks  charge  0.1%  for  collection.    What  are  the  proceeds? 

3.  The  Arithmetic  Publishing  Company  draws  on  K.  T. 
Jewett  for  $150.  The  banks  charge  0.2%  tor  collection. 
What  are  the  proceeds?     Write  the  draft. 


COMMERCIAL  DRAFTS  171 

4.  Eobertson  Bros,  draw  on  J.  P.  Shipley  for  $37.50. 
The  charges  for  collection  are  10/.  This  is  what  per  cent 
of  the  face? 

5.  M.  D.  St.  John  collects  a  $150  debt  through  the  bank, 
the  proceeds  being  $149.70.  What  is  the  bank's  rate  for 
collecting  this  debt  ? 

6.  S.  L.  James  of  Des  Moines  draws  on  L.  D.  Richards 
of  Cedar  Rapids,  Iowa,  for  $75.  The  bank  charges  J%  for 
collecting.    What  are  the  proceeds  ? 

7.  M.  T.  Snell  of  Cleveland  is  the  drawee  of  a  $200 
draft;  The  Farmers  Trust  Co.  of  Detroit  is  the  payee; 
The  World  Soap  Co.  is  the  drawer.    Write  the  draft. 

8.  A.  B.  Stanley  owes  M.  S.  Stanton  for  2  doz.  suits 
@  $113.50;  1^  doz.  suits  @  $130;  2  doz.  overcoats  @  $139; 
7 J  doz.  pairs  trousers  @  $40.  Stanton  draws  on  Stanley 
for  the  money,  and  the  bank  charges  him  50/  for  collecting. 
What  rate  is  this? 

9.  Suppose  William  Bentley  of  Winnipeg,  Manitoba, 
owes  you  $250,  and  you  wish  to  draw  upon  him  for  this 
amount.  Write  out  a  draft,  payable  to  the  order  of  some  bank 
near  your  home.  If  the  bank  charges  xV%  ^^^  collecting, 
what  are  the  proceeds? 

10.  R.  H.  Dudley  owes  Cay  ley  &  Co.  for  4  dressers  @  $14, 
and  6  washstands  @  $3.50,  all  less  15%,  and  a  bedroom 
set  at  $34.55  net.  They  draw  on  him  for  the  amount,  the 
bank  charging  10/  for  collecting.  What  is  the  net  amount 
received  by  Cayley  &  Co.  ? 

11.  R.  J.  Doane  of  Montreal  owes  A.  D.  Kane  of  Pitts- 
burg for  10  steel  girders  @  $50,  and  tells  the  latter  to 
draw  upon  him  for  the  amount.  Mr.  Kane  keeps  his  account 
at  the  Iron  Exchange  Bank.  Make  out  a  draft  for  Mr.  Kane. 
What  is  the  bank's  charge  for  collecting,  at  0.1^%  ? 


172  EXCHANGE 

150.  The  rates  of  exchange.  A  money  order  is  always  sold 
at  a  slight  advance  over  its  face,  and  usually  a  bank  draft 
costs  more  than  its  face.  In  each  case  the  variation  from 
the  face  is  called  the  rate  of  exchange. 

151.  Premium.  If  the  rate  of  exchange  is  added  to  the 
face,  exchange  is  at  a  premium,  as  we  have  already  seen. 

152.  Par.  If  there  is  no  rate  of  exchange,  exchange  is 
at  par, 

153.  Discount.  If  the  rate  of  exchange  is  subtracted  from 
the  face,  exchange  is  at  a  discount 

154.  For  small  sums,  say  for  $500  or  less,  New  York,  Chicago, 
or  Philadelphia  exchange  usually  sells  at  a  premium  of  about 
0.1%.  This  is  to  pay  the  bank  for  its  trouble  and  for  the  expense 
of  shipping  the  money  when  its  balance  at  these  cities  gets  low. 
Banks  usually  buy  such  drafts  at  their  face  value,  thus  making 
no  charge  for  cashing  them. 

155.  But  on  large  sums  the  rate  of  exchange  varies.  If  the 
Chicago  banks  owe  the  New  York  banks  $2,000,000,  they  must 
send  that  amount  by  express,  an  expensive  proceeding.  If  a  man 
in  Chicago  at  that  time  wished  to  buy  a  draft  on  New  York  for 
$30,000,  they  would  charge  him  more  than  usual  because  they 
would  have  to  express  that  much  more  to  New  York.  But  if  a 
man  in  New  York  wished  to  buy  a  draft  on  Chicago,  he  might 
buy  it  for  less  than  $30,000  because  the  bank  would  get  its  money 
at  once  and  the  risk  and  expense  of  transmitting  it  would  be 
saved. 

156.  The  prernium  or  discount  is  usually  quoted  as  a  certain 
per  cent  of  the  face  of  the  draft,  but  sometimes  as  so  much  on 
$1000.  In  the  latter  case  the  quotation  of  \%  premium  is  the 
same  as  that  of  $2.50  premium. 

The  explanation  of  the  Clearing  House,  a  place  where  bank  officials 
of  a  city  meet  daily  to  exchange  drafts  and  checks,  and  to  pay 
balances  due  one  another,  is  too  technical  for  most  classes,  and  if 
given  at  all  should  be  explained  verbaily  by  the  teacher. 


DRAFTS  173 

WRITTEN  EXERCISE 

Find  the  cost  of  the  following  drafts : 
1.    $3756.70,  at  par.  2.    $3500,  0.1%  discount. 

3.    $750,  0.2%  premium.      4.    $6750,  ^i^%  premium. 
5.    $2450,  0.1%  premium.    6.    $17,500,  0.2%  discount. 

7.  What  is  the  cost  of  a  draft  on  San  Francisco  for 
$5200  at  j%  discount?    Write  the  draft. 

8.  What  must  be  paid  in  Memphis  for  a  draft  on 
Chicago  for  $3400,  exchange  being  at  J%  premium? 

9.  A  draft  for  $4800  was  bought  for  $4794.  Was  ex- 
change at  a  premium  or  a  discount?    What  was  the  rate? 

10.  When  a  Boston  draft  for  $35,000  can  be  bought  in 
New  Orleans  for  $34,930,  is  exchange  at  a  premium,  at 
par,  or  at  a  discount  ?    What  is  the  rate  ? 

11.  If  J.  K.  Glover  draws  on  J.  B.  Thornton  for  $250, 
and  the  banks  charge  0.1%  for  collection,  what  are  the 
net  proceeds  that  Glover  will  receive  ?    Write  the  draft. 

12.  My  agent  in  Toronto  sells  a  house  for  me  for  $2500. 
He  charges  2%  commission,  and  the  bank  charges  $2.50 
premium  for  a  draft  for  any  amount  between  $2000  and 
$2500.    What  sum  does  he  remit  to  me? 

13.  A  telegraphic  money  order  costs  twice  the  rate  for  a 
ten-word  message,  plus  1%  premium  on  the  face.  A  ten- 
word  message  from  Kansas  City  to  Albany  costs  50  ct. 
What  will  a  telegraphic  money  order  for  $375  cost? 

14.  Mr.  Edgcomb  of  Denver  owes  Mr.  Nourse  $3243.24 
in  that  city.  Mr.  Nourse  has  gone  to  New  York  on  business 
and  asks  that  the  money  be  sent,  less  the  cost  of  exchange. 
Exchange  being  at  0.1%  premium,  what  is  the  face  of  the 
draft? 


174  EXCHA^^GE 

157.  Foreign  exchange.    If  a  man  buys  foreign  goods,  he 
often  has  to  send  money  abroad. 

158.  Table  of  English  money : 

12  pence  (d.)  =  1  shilling  (s.)  =  $0,243  +. 

20  shillings    =  1  pound  (£)    =  $4.8665. 
We   commonly  think  of  the  pound  as  about  $5,  the  shilling 
as  about  25;^,  and  the  penny  as  about  2^.     Canada  uses  the  same 
table  of  money  as  the  United  States. 

159.  Table  of  French  money  : 

100  centimes  (c.)  =  1  franc  (fr.)  =  $0,193. 
We  commonly  think  of  the  franc  as  20/. 
This  system  is  used  in  several  European  countries. 

160.  Table  of  German  money : 

100  pfennigs  (pf.)  =  1  mark  (M.)  =  $0,238. 
We  commonly  think  of  the  mark  as  25^,  and  4  pf.  as  1^. 

ORAL    EXERCISE 

Taking  the  above  approximate  values^  state  about  how 
much  the  following  sums  represent  in  our  money : 

1.    £7.  2.    £6  5s.  3.    £9  4s.  4.    £8  10s. 

5.    £50.  6.    £10  16s.      7.    £12  2s.         8.    £15 12s. 

9.    £150.      10.    £50  4s.       11.    £60  7s.       12.    £90  9s. 
13.    50  fr.       14.    75  fr.  15.    125  fr.         16.    300  fr. 

17.    800  fr.     18.    1200  fr.       19.    80  M.  20.    100  M. 

21.    240  M.    22.    640  M.        23.    840  M.        24.    1200  M. 
25.    £8  4s.  6d.  26.    £7  2s.  4d.  27.    £5  7s.  9d. 

28.    50  fr.  50  c.         29.    75  fr.  25  c.  30.    80  fr.  20  c. 

31.    8  M.  20  pf.         32.    10  M.  40  pf.        33.    80  M.  4  pf. 
34.    Express  $40  approximately  as  German  money;  as 
English  money  ;  as  French  money. 


FOREIGN  MONEY  175 

WRITTEN   EXERCISE 

Express  as  pence : 

1.    £3.  2.    £2  4s.  3.    £3  5s.  6d. 

4.    3s.  Sd.  6.    18s.  3d.  6.    £5  Is.  2d. 

Express  as  shillings  and  decimals  : 

7.    8s.  8d.  8.    9s.  3d.  9.    £3  6s.  9d. 

Express  as  pounds  and  decimals : 
^  10.    £2  2s.  11.    £3  4s.  12.    £6  4s.  6d. 

Express  as  centimes : 

13.    2b  fr.  14.    37  fr.  15.    35  fr.  30  c. 

Express  as  francs  and  decimals  : 
16.    275  c.  17.    475  c.  18.    1275  c. 

Express  as  marks  and  decimals : 
19.    350  pf.  20.    480  pf.  21.    9275  pf. 

Express  as  pfennigs  : 

22.    175  M.  23.    200  M.  24.    10  M.  75  pf. 

Taking  £1  as  equal  to  $4.87,  express  in  our  money : 
25.    £75.  26.    £68.  27.    £16  10s. 

Taking  <£1  as  equal  to  14.87,  express  in  English  nfioney: 
28.    $38.96.  29.    $24.35.  30.    $43.83. 

Taking  1  M.  as  equal  to  23.8/,  express  in  our  money: 
31.    75  M.  32.    125  M.  33.    3750  M. 

Taking  1 M.  as  equal  to  23.8/,  express  in  German  money: 
34.    $9.52.  35.    $14.28.  36.    $71.40. 

Taking  1  fr.  as  equal  to  19.3/,  express  in  our  money: 
37.    85  fr.  38.    230  fr.  39.    750  fr. 


176  EXCHANGE 

161.  Bills  of  exchange.  Foreign  drafts  are  also  called 
hills  of  exchange. 

162.  Rate  of  exchange.  The  rate  of  foreign  exchange 
varies  continually,  depending  on  the  demand. 

Thus,  when  English  exchange  is  quoted  at  4.90  (that  is,  a  draft 
for  £1  costs  $4.90)  it  is  above  par,  for  4.8665  is  par. 

163.  Foreign  quotations.  English  exchange  is  quoted  at  dollars 
to  the  pound,  as  4.92. 

French  exchange  is  quoted  either  at  francs  to  the  dollar,  5.14 
meaning  that  $1  will  buy  a  draft  for  5.14  francs,  or  at  cents  to 
the  franc,  19.7  meaning  that  a  draft  for  1  fr.  costs  19.7  ct. 

German  exchange  is  quoted  at  cents  to  the  4  marks,  97  mean- 
ing that  a  draft  for  4  M.  costs  97  ct.,  or  at  cents  to  the  mark, 
24.1  meaning  that  a  draft  for  1  M.  costs  24.1  ct. 

164.  At  present  much  of  the  foreign  exchange  for  small  sums 
is  carried  on  by  post-office  or  express  money  orders. 

165.  Newspaper  quotations.  Exchange  is  often  quoted  thus : 

Demand  60  Bays  90  Bays 

Sterling                      4.83  4.79  4.77 

Francs                        5.20  5.21  5.23 

Marks                           94|  94|              93j 

This  means  that  a  £1  draft  on  England  (sterling)  will  cost 
$4.83  if  payable  on  demand  (at  sight),  $4.79  if  payable  60  days 
after  sight,  or  $4.77  90  days  after  sight.  The  quotations  for  the 
following  examples  nlay  be  taken  as  above  or  from  a  newspaper. 

ORAL  EXERCISE 

State  the  cost  of  demand  drafts  for: 

1.    £10.         2.    £5.                3.    £2.  4.  £1000. 

5.    5.20  fr.     6.    52  fr.             7.    104  fr.  8.  5200  fr. 

9.    40  M.      10.    400  M.        11.    4000  M.  12.  40,000  M. 


FOREIGN  EXCHANGE  177 

166.  Illustrative  problems.  1.  What  will  a  60-day  draft 
for  £40  cost? 

1.  £1  costs  84.79. 

2.  £40  cost  40  times  $4.79  =  $191.60. 

2.  What  will  a  demand  draft  for  75  M.  cost? 

1.  4  M.  cost  $0.94f,  1  M.  costs  i  of  $0.94|. 

2.  75  M.  cost  75  times  J  of  $0.94f  =  $17.74. 

3.  What  will  a  90-day  draft  for  125  fr.  cost? 

$1 

1.  5.23  fr.  cost  $1,  1  fr.  costs  — —  • 

5.2o 

$125      ^ 

2.  125  fr.  cost  -— —  =  $23.90. 

5.23 

WRITTEN  EXERCISE 

1.  Find  the  cost  of  a  60-day  draft  for  £90  10s. 

2.  Find  the  cost  of  a  demand  draft  for  305  fr.  50  c. 

3.  Find  the  cost  of  a  90-day  draft  for  750  M. ;  620  M. 

4.  How  large  a  sterling  90-day  draft  will  $71.55  buy? 

5.  How  large  a  demand  draft  on  Paris  will  $125  buy  ? 

6.  How  large  a  60-day  draft  on  Leipzig  will  $76  buy? 

7.  A  merchant  buys  Scotch  tweeds  in  London  to  the 
amount  of  £127  10s.     What  will  a  60-day  draft  cost? 

8.  A  city  library  buys  books  in  Paris  to  the  amount  of 
578  fr.  31  c.  How  much  will  a  draft  for  this  amount  cost 
when  exchange  is  quoted  at  5.21? 

9.  I  have  bought  400  M.  worth  of  books  in  Leipzig. 
Which  is  better  for  me,  to  buy  a  demand  draft  or  an 
express  money  order   @   24/  to  the  mark? 

10.  I  have  bought  a  painting  in  Florence  for  670  lire  (l6ra, 
francs),  and  7  lire  for  packing.-  If  exchange  on  Florence 
is  5.18,  how  much  will  a  draft  for  this  amount  cost? 


178 


METRIC  SYSTEM 


METRIC   SYSTEM 


o 

3S 

CO 

t- 

«o 

\a 

■^ 

CO 

<M 

*"* 

E 

o 

= 

167.  Where  used.  If  a  man  buys  foreign  goods, 
except  from  England,  the  measures  will  probably 
be  a  more  convenient  system  than  ours,  invented 
in  France  about  1800,  and  now  used  in  a  large  part 
of  the  civilized  world.  It  is  easily  learned,  it  is 
much  more  simple  than  our  system,  and  we  need  it 
in  all  scientific  work  and  in  our  newspaper  reading. 
It  is  called  the  Metric  System. 

168.  Meter.  The  unit  of  length  is  the  meter.  It 
is  nearly  39.37  in.  long,  or  nearly  one  ten-millionth 
of  the  distance  from  the  equator  to  the  pole. 

169.  Liter.  The  unit  of  capacity  is  the  liter  (leter), 
a  cube  ^^  of  a  meter  on  an  edge.    It  is  nearly  1  qt. 

170.  Gram.  The  unit  of  weight  is  the  gram.  It 
is  practically  the  weight  of  a  cube  of  water  yi^  of 
a  meter  on  an  edge.    It  equals  nearly  15.4  grains. 

171.  The  prefixes.  The  tables  are  easily  learned 
when  the  prefixes  are  known. 

Just  as  1  mill  =  y^Vir  o^  ^  dollar, 
so  1  millimeter  =  0.001  of  a  meter. 

Just  as  1  cent  =  jj^  of  a  dollar, 
so  1  centimeter  =  0.01  of  a  meter. 

Just  as  decimal  means  tenths, 
so  1  decimeter  =  0.1  of  a  meter. 


S  I 


The  prefix 

MEANS 

AS  IN 

WHICH  MEANS 

myria- 

10,000 

myriameter 

10,000 

meters. 

kilo- 

1000 

kilogram 

1000 

grams. 

liekto- 

100 

hektoliter 

100 

liters. 

deka- 

10 

1 

0.1 

dekameter 

10 
1 
0.1 

meters. 

deci- 

decimeter 

of  a  meter. 

centi- 

0.01 

centigram 

0.01 

of  a  gram. 

milli- 

0.001 

millimeter 

0.001 

of  a  meter. 

TABLE  OF  LENGTH  179 

172.  Table  of  length : 

A  myriameter  =  10,000  meters. 

A  kilometer  (km.)  =  1000       *' 

A  hektometer  =  100       *' 

A  dekameter  =  10       *' 

Meter  (m.) 

A  decimeter  (dm.)  =  0.1      of  a  meter. 

A  centimeter  (cm.)  =  0.01             *' 

A  millimeter  (mm.)  =  0.001           " 

In  the  tables  the  most  important  names  are  in  heavy  type. 

173.  Approximate  values.  The  meter  is  about  39.37  in.,  3^  ft., 
or  a  little  over  a  yard  ;  the  kilometer  is  about  0.6  of  a  mile. 

174.  Abbreviations.  The  abbreviations  in  this  book  are  recom- 
mended by  various  scientific  associations.  Some,  however,  use 
Km.,  Dm.,  dm.,  for  kilometer,  dekameter,  and  decimeter. 

ORAL  EXERCISE 

Express  as  meters  and  decimals: 

1.    1  km.                      2.    Q5  km.  3.  225  dm. 

4.  375  dm.                   5.    700  dm.  6.  750  km. 

7.    3275  cm.                8.  4550  cm.  9.  6500  cm. 

10.    120,000  mm.       11.    216,500  mm.  12.  100,575  mm. 

Express  approximately  as  meters  (1  m.  =  3^  ft.  =  39  in.): 
13.    13  ft.  14.   39  ft.  15.    Qb  ft. 

16.    3.9  in.  17.    78  in.  18.    390  in. 

19.    325  ft.  20.    650  ft.  21.    0.39  in. 

22.    9  ft.  9  in.  23.    975  ft.  24.    3  ft.  3  in. 

Express  approximately  as  feet^  inches,  or  miles: 
25.    8  m.  26.    24  m.  27.    \  km.         28.    f  km. 

29.    100  km.       30.    300  km.     31.    60  km.       32.    0.5  m. 
33.    30.5  km.       34.    20.5  km.    35.    100  m.       36.    1200  km. 


180  METRIC  SYSTEM 

WRITTEN  EXERCISE 

Express  as  meters  and  decimals: 
J  1.    275.3  mm.  2.    476.4  cm.  3.    293.8  dm. 

Express  as  kilometers  and  decimals: 

4.    4862  m.  5.    12,758  cm.         6.    628,341  mm. 

7.    47  mi.  8.    2^.5  mi.  9.    10,560  ft. 

Express  as  miles : 

10.    751  km.  11.    286  km.  12.    34.9  km. 

13.    5280  m.  14.    2976  m.  15.    14,781  dm. 

Express  as  feet^  taking  3i  f t.  =  1  m. : 
16.    17  m.  17.    64  m.  18.    108  m. 

19.    6894  cm.  20.   2986  cm.  21.    81,296  mm. 

Express  as  inches^  taking  39.37  in.  =  l  m.: 
22.    47  m.  23.    324  cm.  24.    4680  mm. 

25.    34.5  m.  26.    2.83  cm.  27.    3000  mm. 

28.  Express,  the  diameter  of  a  7-cm.  gun  in  inches. 

29.  A  certain  hill  is  203  m.  high.    Express  this  in  feet. 

30.  A  certain  tower  in  Paris  is  37.5  m.  high.  Express 
this  in  feet. 

31.  The  distance  from  Dieppe  (De-ep')  to  Paris  is  209  km. 
Express  this  in  miles. 

32.  The  distance  between  two  places  in  Germany  is 
178  km.     Express  this  in  miles. 

33.  The  distance  from  Paris  to  Cologne  is  306  mi.  What 
is  the  railway  fare  at  12  centimes  per  kilometer  ? 

34.  The  distance  from  Paris  to  Brussels  is  326  km.,  and 
it  takes  7  hours  to  make  the  trip  by  railway.  What  is  the 
average  number  of  miles  an  hour  ? 


SQUARE  MEASURE  181 

175.  Table  of  square  measure : 

A  square  myriameter  =  100,000,000  square  meters. 

*'        kilometer  (km2.)     =      1,000,000      "  *' 


"        hektometer             = 

10,000      "          *' 

"        dekameter               = 

100      "          " 

Square  meter  (m^.) 

A  square  decimeter  (dm2.)     = 

0.01         of  a  square  meter. 

'*        centimeter  (cm2.)    = 

0.0001               "              *' 

"        millimeter  (mm2.)  = 

0.000001 

The  abbreviation  sq.  m.  is 

often  used  for  m^. 

176.  Land  measure.  The  square  dekameter  is  also  called 
an  are  (ar)  ;  and  since  there  are  100  square  dekameters  in 
1  hm^.,  a  square  hektometer  is  called  a  hektare  (ha.).  The 
hektare  equals  2.47  acres  =  nearly  2J  acr'^.s. 

ORAL  EXERCISE 

Express  as  square  meters : 
1.  2  km^.  2.  30,000  cm^.       3.  5  square  dekameters. 

4.  1000  dml       5.  100,000  cm^.     6.  2  square  hektometers. 

Express  as  square  dekameters  : 
7.  5000  m^.         8.  2  km^.  9.  5  square  hektometers. 

Express  as  hektares  : 
10.  10,000  m'^.    11.  Ikm^.  12.  5  square  hektometers. 

Express  as  hektares,  taking  1  ha.  =  21-  A. : 
13.  5  A.  14.  25  A.  15.  100  A.  16.  50  A. 

WRITTEN  EXERCISE 

Express  as  square  centimeters: 

1.  750  km^.        2.  37  m^.        3.  4296  mm^.        4.  6.25  m^. 

5.  France  has  an  area  of  322,335  km^.    How  many  acres? 


182  METRIC  SYSTEM 

177.  Table  of  cubic  measure : 

A  cubic  myriameter             =  10^2  cubic  meters. 

*'       kilometer                =  lO^      "          ** 

"•       hektometer             =  1,000,000       *'  " 

'<•       dekameter               =  1000       "          " 

Cubic  meter  (m^.) 

A  cubic  decimeter  (dms.)     =  0.001             of  a  cubic  meter. 

'*       centimeter  (cm3.)    =  0.000001              "             " 

*'        millimeter  (mm^.)  =  0.000000001         *'             *' 

178.  The  stere.  The  cubic  meter  is  also  called  a  stere 
(ster,  St.),  a  unit  used  in  measuring  wood. 

ORAL   EXERCISE 

Uxpress  as  cubic  meters  : 

1.    17  St.  2.    5000  dml  3.    2,000,000  cra^ 

4.    1000  dm^  5.    2  cubic  dekameters. 

Express  as  cubic  decimeters: 

6.    7  m^.  7.    8  St.  8.    5000  cm«. 

9.    19  m\  10.    26  St.  11.    10,000  cm^. 

12,  How  many  centimeters  in  a  meter?  square  centi- 
meters in  a  square  meter?  cubic  centimeters  in  a  cubic 
meter  ?    cubic  decimeters  in  a  cubic  dekameter  ? 

13.  Estimate  the  length,  width,  and  height  of  your  school- 
room, in  meters.    How  many  cubic  meters  in  the  room? 

WRITTEN   EXERCISE 

Express  as  cubic  meters: 
1.    19.75  cubic  dekameters.  2.    427,653.84  mm«. 

3.  37.5  St. +98.9  St. +764  st. +27.43  st.+196.8  st.+37st. 

4.  0.000001  cubic  hektometer.     5.    0.0000001  km^. 
6.    34|^  cu.  ft.  (calling  3J  ft.  equal  to  1  m.). 


WEIGHT  183 

179.  Table  of  weight : 

A  metric  ton  (t.)      ^=  1,000,000  grams. 

A  quintal  (q.)          =  100,000 

A  myriagram           =  10,000 

A  kilogram  (kg.)      =  1000 

A  hektogram           =  100 

A  dekagram             =  10 

Gram  (g.) 

A  decigram              =  0.1         of  a  gram. 

A  centigram    (eg.)  =  0.01             " 

A  milligram  (mg.)  =  0.001           " 

The  metric  ton  is  nearly  the  weight  of  1  ms.  of  water  at  its 
greatest  density  ;  the  kilogram,  of  1  dm^. ;  and  the  gram,  of  1  cm3. 

180.  Approximate  values.    A  kilogram  is  about  2^  lb.    A 
5-ct.  piece  weighs  5  g.    A  metric  ton  is  nearly  2204.6  lb. 

ORAL   EXERCISE 

Express  as  grams : 
1.    147  eg.  2.    3400  mg.  3.    5200  eg. 

4.    348  kg.  5.    2950  kg.  6.    1728  kg. 

Express  as  centigrams: 
7.    121  g.  8.    3  kg.  9.    19  kg. 

10.   20  mg.  11.    135  mg.  12.    6800  mg. 

Express  as  milligrams: 

13.    3.75  g.  14.    4.25  g.  15.    55.2  eg. 

Express  as  kilos  (kilograms): 

16.    17  t.  17.    3.5  t.  18.    4.25  t. 

19.    18,000  eg.  20.    15,000  mg.        21.    2460  g. 

Express  as  pounds: 

22.    25  kg.  23.    30  kg.  24.   50  kg. 

25.    500  kg.  26.    100  kg.  27.    125  kg. 


k 


184  METRIC  SYSTEM 


WRITTEN  EXERCISE 


Express  as  kilos  (kilograms): 
1.    374  lb.  2.    352  oz.  3.   3275  g. 

4.    15,428  lb.  5.   48.4  lb.  6.    7275  g. 

7.    IT.  204  1b.  8.    300,000  eg.  9.    173.8  1b. 

10.  What  is  the  weight  of  35  dm^.  of  water  in  pounds? 

11.  How  many  5-ct.  pieces  will  it  take  to  weigh  a  kilo? 

12.  Express  a  gram  as  a  fraction  of  an  ounce ;  of  a  pound. 

13.  In  traveling  on  the  continent  of  Europe,  25  kg.  of 
baggage  is  usually  transported  free.    How  many  pounds  ? 

14.  What  is  the  weight,  in  metric  tons,  of  water  in  a 
tank  2,b  m.  by  3  m.  by  1.5  m.  ?  3.4  m.  by  6  m.  by  4.25  m.? 

15.  What  is  the  weight,  in  metric  tons,  of  water  in  a 
tank  5.2  m.  by  3.4  m.  by  IJ  m.  ?  2.8  m.  by  4  m.  by  0.75  m.  ? 

16.  Steel  being  7.8  times  as  heavy  as  water,  what  is  the 
weight  of  a  bar  of  steel  7.8  cm.  wide,  3.1  cm.  thick,  and 
1.5  m.  long? 

The  number  7.8  is  called  the  specific  gravity  of  steel.  From 
Exs.  18  and  19  the  specific  gravity  of  lead  is  11.3,  and  of  gold  19.3. 

17.  The  specific  gravity  of  granite  being  2.7,  what  is 
the  weight  of  a  block  of  granite  1.2  m.  by  0.75  m.  by  0.25  m.  ? 

18.  Lead  being  11.3  times  as  heavy  as  water,  what  is 
the  weight  of  a  bar  of  lead  3.3  cm.  square  on  the  end,  and 
26,^  cm.  long? 

19.  Gold  being  19.3  times  as  heavy  as  water,  how  many 
grams  does  a  cube  of  gold  3  cm.  on  an  edge  weigh  ?  Express 
the  result  also  as  a  fraction  of  a  kilogram. 

20.  A  man  traveling  abroad  steps  on  a  penny-in-the-slot 
weighing  machine  and  finds  he  weighs  75  kg.  How  many 
pounds  does  he  weigh? 


0.1      c 

►f  a  liter. 

0.01 

(( 

0.001 

(( 

CAPACITY  185 

181.  Table  of  capacity: 

A  hektoliter  (hi.)     =  100  liters. 
A  dekaliter  =    10     " 

Liter  (1.) 
A  deciliter 
A  centiliter 
A  milliliter  (ml.) 

182.  Approximate  values.  A  liter  is  the  same  as  1  dm^ 
Hence  1  1.  of  water  weighs  1  kg.  A  liter  is  practically  the 
same  as  our  quart. 

ORAL   EXERCISE 

Express  as  liters: 

1.    5000  ml.  2.  3  hi. 

4.    2500  ml.  5.  7.5  hi. 

7.    5  gal.  8.  8  pt. 

Express  as  hektoliters : 
10.   250  1.  11.   375  1. 

13.    2575  1.  14.    3500  1. 

16.    300  qt.  17.    2600  qt. 

Express  as  quarts: 

19.    175  1.  20.    16.25  1. 

22.    20.75  1.  23.    12.50  hi. 

Express  in  kilograms  the  weight  of  the  following  amounts 
of  water : 

25.    25.5  1.  26.    18.75  1.  27.    16  hi. 

28.    17.50  1.  29.    26.50  hi.  30.    0.01  hi. 

31.  How  many  decimeters  in  a  meter  ?  How  many  cubic 
decimeters  in  a  cubic  meter?  How  many  liters  in  a  cubic 
meter  ?    A  cubic  meter  of  water  weighs  how  many  kilos  ? 


3. 

17  hi. 

6. 

2.25  hi. 

9. 

121  gal. 

12. 

125.5  1. 

15. 

625.3  1. 

18. 

50  gal. 

21. 

4  hi. 

24. 

0.8  hi. 

186  METRIC  SYSTEM 

WRITTEN  EXERCISE 

1.  Milk  weighing  1.032  times  as  much  as  water,  how 
many  kilos  does  7  1.  weigh? 

2.  Alcohol  being  0.83  as  heavy  as  water,  find  the  weight 
of  7  1.    Express  the  result  in  kilos  ;  in  pounds. 

3.  The  Eiffel  Tower  in  Paris  is  300  m.  high.  Express 
this  as  inches ;  as  feet ;  as  a  fraction  of  1  km. 

4.  Gold  being  19.3  times  as  heavy  as  water,  how  much 
does  17.5  cm^  weigh?    Answer  in  grams;  in  grains. 

5.  Cork  being  one  fourth  as  heavy  as  water,  how  much 
does  9  dm^  of  cork  weigh?    Answer  in  kilos ;  in  pounds. 

6.  The  specific  gravity  of  silver  (see  page  184,  Ex.  16) 
being  10.5,  what  is  the  weight  of  a  piece  of  silver  12.5  cm. 
by  7.2  cm.  by  3.1  cm.  ? 

7.  The  specific  gravity  of  petroleum  being  0.7,  what  is 
the  weight  of  7.34  dm^  of  petroleum? 

8.  The  specific  gravity  of  alcohol  being  0.79,  what  is 
the  weight  of  alcohol  in  a  tank  5  dm.  by  3  dm.  by  2.5  dm.  ? 

9.  The  specific  gravity  of  copper  being  8.9,  what  is  the 
weight  of  a  piece  of  copper  1  m.  by  2  dm.  by  9  cm.? 

10.  One  piece  of  land  is  20  m.  long,  and  30  m.  wide,  and 
another  is  20  yd.  long  and  30  yd.  wide.  Find  the  area  of 
the  first  in  hektares  and  the  second  in  acres. 

11.  Samples  of  merchandise  may  be  sent  abroad  by  mail 
if  they  do  not  weigh  more  than  350  g.  Express  this  as  a 
fraction  of  a  pound  ;  as  ounces ;  as  a  fraction  of  1  kg. 

12.  Find  in  kilos  the  weight  of  water  in  a  tank  3  m.  by 

2  m.  by  5  m. ;  also  the  weight  in  pounds  of  water  in  a  tank 

3  ft.  by  2  ft.  by  5  ft.    (1  cu.  ft.  of  water  weighs  62,5  lb. 
Notice  the  simplicity  of  the  metric  system.) 


REVIEW 


187 


Mr.  Field's  Trip  to  Europe 

Mr.  and  Mrs.  Field  took  a  vacation  trip  to  Europe,  landing  at 
Liverpool,  traveling  through  England,  France,  Germany,  Switzer- 
land, and  Italy,  and  sailing  home  from  Naples.  After  leaving  Eng- 
land   they    found  f,i 


the  Metric  Sys- 
tem used  by  every 
one,  and  of  course 
they  did  not  meet 
our  system  of 
money  until  they 
landed  in  New 
York  again.  They 
found  that  Swit- 
zerland and  France 
used  the  same  sys- 
tem of  money,  and 
that  Italy  had  the 
same  values,  but 

called  the  franc  a  lira  (le-ra;  plural,  /ire,  le-ra).  In  making  esti- 
mates in  our  own  system  they  allowed  $5  to  £1,  25^  to  Is.,  2^  to 
Id.,  25;^  to  1  M.,  20;^  to  the  franc  or  lira,  1 J^  yd.  or  3J  ft.  to  1  m., 
I  mi.  (0.6  mi.)  to  1  km.,  and  2^  lb.  (2.2  lb.)  to  1  kg. 


ORAL  EXERCISE 

1.  At  $90  a  steamer  ticket  each  way,  less  10%  on  the 
return  portion  of  the  ticket,  what  did  both  tickets  cost  ? 

2.  On  the  voyage  to  Liverpool  he  gave  £3  5s.  for 
stewards'  fees.    How  many  dollars  did  he  give  ? 

3.  He  landed  in  Liverpool  at  2  p.m.,  and  at  once  tele- 
graphed his  brother  in  San  Francisco  and  his  sister  in 
New  York.  Allowing  an  hour  for  delay,  at  what  time 
did  the  messages  reach  their  respective  destinations? 


I 


188  REVIEW 

4.  He  paid  21s.  9d.  a  ticket  from  Liverpool  to  London. 
How  much  did  he  pay  for  the  two  tickets?  How  many 
dollars  ? 

5.  He  paid  the  cab  driver  in  London  2s.  6d.  to  take 
them  to  their  hotel.    How  much  is  this  in  our  money  ? 

6.  He  paid  12s.  a  day  for  each,  at  one  of  the  smaller 
hotels.  They  remained  there  a  week.  How  much  did  it 
cost  the  two  ?    How  much  in  our  money  ? 

7.  He  paid  33s.  each  for  two  tickets  to  Paris.  How 
much  did  he  pay  for  both  ?    How  much  in  our  money  ? 

8.  At  Paris  he  paid  the  cab  driver  2  fr.  50  c.  to  take 
them  to  their  hotel.    How  much  is  this  in  our  money? 

9.  He  paid  14  fr.  a  day  for  each,  at  a  hotel  near  the 
Arch  of  Triumph,  and  they  spent  11  days  in  Paris.  How 
much  was  the  hotel  bill  ?    How  much  in  our  money  ? 

10.  The  Arch  of  Triumph  is  50  m.  high.  How  many 
feet  high?  It  is  at  the  end  of  a  beautiful  avenue  2.2  km. 
long.    Express  this  distance  in  miles. 

11.  Not  far  from  his  hotel  is  the  Eiffel  Tower,  300  m. 
high.    Express  this  height  in  feet. 

12.  The  distance  from  Paris  to  Cologne  is  510  km. 
Express  this  distance  in  miles. 

13.  He  bought  two  tickets  at  44  fr.  each.  How  much 
did  they  cost  ?    How  much  in  our  money  ? 

14.  They  reached  Cologne  at  5  :  30  p.m.  (Mid-European 
time,  15°  E.).  What  time  (standard)  was  it  then  in  Eng- 
land? in  Boston?  in  Chicago?  in  Portland,  Oregon? 

15.  They  spent  two  days  in  Cologne,  paying  12  M.  each 
per  day.  How  much  was  the  hotel  bill?  How  much  in 
our  money  ? 


REVIEW  189 

16.  At  Cologne  Mrs.  Field  did  some  shopping,  spending 
150  M.    How  much  is  this  in  our  money? 

17.  Among  her  purchases  was  some  silk  for  a  gown. 
She  bought  18  m.    How  many  yards  ? 

18.  From  Cologne  they  went  up  the  Rhine  to  Mainz,  a 
distance  of  150  km.    How  many  miles  ? 

19.  The  tickets  from  Cologne  to  Mainz  were  15  M. 
50  pf.  each.    What  did  the  two  cost?    How  many  dollars? 

20.  They  spent  two  days  at  Mainz,  paying  14  M.  each  per 
day.    How  much  was  the  hotel  bill  ?    How  many  dollars  ? 

21.  They  then  went  to  Lucerne,  a  distance  of  400  km. 
How  many  miles? 

22.  The  tickets  to  Lucerne  cost  32  M.  apiece.  How 
much  did  the  two  cost  ?    How  many  dollars  ? 

23.  They  spent  two  weeks  in  Switzerland,  their  expenses 
averaging  22  fr.  50c.  apiece  per  day.  How  much  were  they 
for  two  ?  How  many  dollars  ?  How  many  dollars  for  the 
two  weeks? 

24.  Their  tickets  from  Lucerne  right  through  to  ]S"aples, 
including  Florence  and  Rome,  cost  100  fr.  apiece.  How 
much  for  the  two  tickets?    How  many  dollars? 

25.  They  spent  three  weeks  in  Italy,  their  expenses 
averaging  20  fr.  apiece  per  day.  How  much  were  they  for 
two?    How  many  dollars? 

2  6.  Their  other  purchases  and  extras  in  England  amounted 
to  £S,  in  France  to  125  fr.,  in  Germany  to  120  M.,  in 
Switzerland  to  60  fr.,  and  in  Italy  to  80  lire.  Express  each 
in  dollars. 

WRITTEN  EXERCISE 

Taking  the  expenses  as  stated  in  the  Oral  Exercise,  find 
the  cost  of  the  trip  taken  by  Mr.  and  Mrs.  Field. 


190  TAXES 


TAXES 


183.  What  are  taxes  ?  Whatever  a  man's  occupation,  one 
of  his  expenses  will  be  taxes,  money  paid  for  the  support 
of  the  village,  town,  city,  county,  or  state. 

184.  Expenses  of  our  government.  The  expenses  of  the 
United  States  government  vary  from  year  to  year,  but 
they  average  about  $1,300,000  a  day,  or  $473,500,000  a 
year.  Some  items  of  our  income  and  expenditures  are  as 
follows,  varying  from  year  to  year : 

Income : 

Customs  (duties  on  imported  goods)        .     ^275,000,000 
Internal  revenue  (tobacco,  etc.)      .     .     .       275,000,000 

Sale  of  public  lands 7,500,000 

Miscellaneous 36,000,000 

Expenditures.' 

War  Department $112,000,000 

Navy  Department         88,000,000 

Pensions 138,000,000 

Indians 10,000,000 

Salaries,  diplomatic  service,  etc.     .     .     .       150,000,000 

WRITTEN  EXERCISE 

1.  When  our  income  is  $575,000,000  and  our  customs 
receipts  are  $242,000,000,  these  receipts  are  what  per  cent 
of  the  income  ? 

2.  Taking  our  expenditures  as  $488,000,000  a  year,  what 
per  cent  of  this  goes  to  the  War  Department,  as  above 
stated  ?  to  the  Navy  Department  ?  to  pensions  ? 

3.  The  colleges  and  universities  of  the  country  cost 
$23,850,000  a  year,  and  are  not  supported  by  the  govern- 
ment.   This  is  what  per  cent  of  the  $488,000,000  in  Ex.  2  ? 


GOVERNMENT  INCOME  AND  EXPENSES   191 

4.  Our  income  from  public  lands  is  what  per  cent  of 
that  from  our  customs  ? 

In  this  and  Exs.  5-8,  use  the  items  as  given  on  page  190. 

5.  Our  public  lands  receipts  are  what  per  cent  less  than 
the  income  from  internal  revenue? 

6.  Our  income  from  internal  revenue  is  what  per  cent 
greater  than  that  from  our  public  lands? 

7.  What  per  cent  of  our  internal  revenue  would  be 
necessary  to  pay  the  Navy  Department  expenditures  ? 

8.  What  per  cent  of  our  customs  receipts  would  be 
necessary  to  pay  the  War  Department  expenditures  ? 

9.  In  a  certain  year  the  government  paid  $69,210,000 
for  carrying  the  mails,  and  33%  as  much  for  salaries  to 
postmasters.    How  much  did  it  pay  for  both  of  these  items  ? 

10.  The  income  of  the  Post-Office  Department  through  the 
New  York  and  Brooklyn  offices  in  a  certain  year  amounted 
to  $16,206,000.  This  was  what  per  cent  of  the  total  income 
($146,000,000)  of  the  department  that  year? 

11.  In  a  certain  year  the  government  received  $135,- 
810,015  from  taxes  on  spirits,  33%  as  much  from  taxes  on 
tobacco,  and  10%  more  on  fermented  liquors  than  on  tobacco. 
What  were  its  total  receipts  from  these  three  sources  ? 

12.  In  a  certain  year  the  internal  revenue  receipts  of 
the  country  amounted  to  $233,000,000.  The  largest  amount 
paid  by  any  state  was  23%,  paid  by  Illinois.  What  was 
this  amount?     What  did  the  rest  of  the  country  pay? 

13.  In  a  certain  year  the  government  received  $143,820,- 
000  from  the  sale  of  postage  stamps  and  money  orders, 
which  was  94%  of  the  expenses  of  the  Post-Office  Depart- 
ment. How  much  deficiency  did  Congress  have  to  vote  to 
the  Post-Office  Department  that  year  ? 


192  TAXES 

185.  Our  post-oflSlce  system.  We  do  not  often  think  of  our 
post-offices  as  places  where  we  all  pay  taxes  (when  we  buy 
postage  stamps).  The  department  is  nearly  supported  by 
such  receipts.  In  the  following  miscellaneous  problems  the 
annual  income  may  be  taken  as  $150,000,000,  and  the 
number  of  pieces  of  mail  matter  handled  as  9  billion,  but 
the  figures  vary  from  year  to  year. 

WRITTEN  EXERCISE 

1.  The  average  number  of  mistakes  reported  against 
clerks  who  handle  the  mails  is  only  5  out  of  57,500  pieces. 
What  is  the  per  cent  of  errors  ? 

2.  If  the  post  offices  issue  46  million  domestic  money 
orders  a  year,  amounting  to  $358,800,000,  what  is  the 
average  amount  of  each  money  order? 

3.  If  the  receipts  of  the  New  York  post  office  amount 
to  $13,650,000  a  year,  this  is  what  per  cent  of  our  total 
annual  postal  income  as  stated  above? 

4.  How  much  does  it  cost  to  register  a  letter  or  parcel  ? 
If  the  post  offices  transmit  22,831,400  registered  letters 
and  parcels  annually,  what  is  the  income  from  this  source  ? 

5.  If  we  have  75,000  post  offices,  what  is  the  average 
annual  income  for  each  ?  If  the  sum  of  the  salaries  of  the 
postmasters  is  $22,200,000,  what  is  their  average  salary? 

6.  If  the  number  of  postal  routes  is  35,000,  averaging 
14.5  miles  each,  what  is  their  total  length?  If  the  average 
number  of  annual  trips  over  each  route  is  936,  what  is  the 
total  distance  traveled? 

7.  If  the  contractors  who  carry  the  mail  receive  over 
the  stage  mail  routes  6.58/  per  mile  traveled,  how  much 
will  a  contractor  receive  a  year  who  travels  25  miles  daily, 
except  52  Sundays? 


ARMY  AND  NAVY  193 

186.  Our  army  and  navy.  It  is  necessary  for  us  to  keep 
a  navy  and  a  small  army  of  sufficient  strength  to  protect 
us  from  foreign  attack.  It  is  an  expense  and  therefore  is 
considered  under  taxes,  with  certain  review  problems. 

WRITTEN  EXERCISE 

1.  Two  of  our  naval  cruisers  cost  together  $6,810,000, 
one  costing  H^t^^j-^  more  than  the  other.  What  did  each 
cost? 

2.  Gun  metal  is  composed  of  11  parts  of  copper  to  2  parts 
of  tin.  How  much  tin  must  be  added  to  2607  lb.  of  copper 
to  make  gun  metal? 

3.  The  bronze  trimmings  of  the  guns  are  composed  of  17 
parts  of  copper  to  4  parts  of  tin.  How  much  copper  must 
be  added  to  108  lb.  of  tin  to  make  bronze  ? 

4.  A  certain  battle  ship  carries  2000  short  tons  of  coal. 
How  many  pounds  is  this?  If  it  is  12|||%  of  the  loaded 
weight  of  the  ship,  what  is  this  weight? 

5.  The  speed  of  a  19-knot  battle  ship  is  20|%  less  than 
that  of  a  fast  mail  boat.  How  long  would  it  take  the  mail 
boat  to  overtake  it,  giving  the  battle  ship  120  knots  the 
start? 

6.  The  battle  ships  Connecticut,  Kansas,  Louisiana,  Min- 
nesota, and  Vermont  cost  $4,200,000  each.  The  amount 
paid  for  these  five  ships  would  send  how  many  men  through 
an  agricultural  or  trade  school,  at  $1400  each? 

7.  If  our  government  pays  for  the  War  and  Navy  De- 
partments $207,000,000  a  year,  this  is  how  many  times 
the  $9,000,000  annually  paid  by  our  people  to  educate 
their  children  in  colleges  and  universities?  The  tuition  is 
what  per  cent  of  the  war  and  navy  expenses  ? 


194  TAXES 

8.  If  our  swiftest  torpedo  boat  makes  31.395  knots  an 
hour,  which  is  36J%  faster  than  our  best  cruiser,  what  is 
the  speed  of  the  latter  ? 

9.  The  7-in.  guns  are  protected  by  6.9-in.  steel  armor, 
which  is  68fW%  as  thick  as  that  protecting  the  12-in.  guns. 
How  thick  is  the  latter? 

10.  A  12-in.  gun  weighs  64  T.  719  lb.  and  fires  a  1000-lb. 
projectile  with  487  lb.  of  powder.  How  many  pounds  does 
it  weigh  when  loaded?  (Always  use  the  2000-lb.  ton  unless 
otherwise  directed.) 

11.  The  cruiser  Minneapolis  is  21yi^%  faster  than  the 
19-knot  battle  ship  Georgia.  At  these  rates,  if  the  battle 
ship  has  288  knots  the  start,  how  long  will  it  take  the 
cruiser  to  overtake  it  in  a  race? 

12.  One  of  our  battle  ships  has  four  12-in.  guns,  or  20% 
as  many  as  it  has  7-in.  guns.  The  rest  of  its  guns  are 
3-in.  The  12-in.  and  7-in.  guns  together  are  54^^%  of  the 
total  number.    How  many  7-in.  and  3-in.  guns  are  there  ? 

13.  A  shot  from  a  certain  12-in.  gun  exerts  enough  force 
at  the  muzzle  to  lift  a  weight  of  46,240  tons  to  the  height 
of  1  ft.  This  is  70%  more  force  than  that  exerted  by  a 
certain  10-in.  gun.    Find  the  force  exerted  by  the  latter. 

14.  A  16-in.  gun  fires  a  projectile  over  5  ft.  long,  weigh- 
ing 1  T.  400  lb.,  with  576  lb.  of  smokeless  powder.  At  $1 
a  pound  for  such  powder,  and  5/  a  pound  for  the  projectile, 
how  much  does  it  cost  the  government  to  fire  such  a  gun 
once?    to  fire  it  a  dozen  times? 

15.  One  ship  fired  a  signal  to  another,  which  was  answered 
as  soon  as  it  was  heard.  The  first  ship  heard  the  answer- 
ing gun  181  sec.  after  the  first  gun  was  fired.  What  was 
the  distance  between  the  ships,  sound  traveling  (at  the 
temperature  then  observed)  1142  ft.  per  second  ? 


TARIFF  195 

187.  Tariff.  The  United  States  collects  a  large  part  of  its 
income  by  a  tax  on  goods  brought  into  the  country.  This 
income  is  called  customs  revenue^  ^«^!#j  or  duty, 

188.  Customhouse.  Customs  revenue  is  collected  at  custom- 
houses.    These  are  situated  Sit  ports  of  entry, 

189.  Classes  of  goods.    Goods  imported  may  be  : 

1.  On  the  free  list,  and  not  subject  to  duty,  as  raw  silk. 

2.  Subject  to  ad  valorem  (on  the  value)  duty,  a  certain 
per  cent  on  the  value  at  the  place  of  purchase,  as  clocks, 
on  which  the  duty  is  40%  ad  valorem. 

3.  Subject  to  specific  duty,  a  certain  amount  per  bushel, 
etc.,  as  potatoes,  on  which  the  duty  is  25  f  a  bushel. 

4.  Subject  to  both  ad  valorem  and  specific  duty,  as  velvet 
carpets,  the  duty  being  60/  per  square  yard  plus  40 ^j;^. 

ORAL   EXERCISE 

State  the  duty  on  the  following  : 

1.  750  T.  of  hay,  duty  $4  per  ton. 

2.  $275  worth  of  goods,  duty  10%. 

3.  $484  worth  of  goods,  duty  25%. 

4.  $800  worth  of  goods,  duty  40%. 
6.  $325  worth  of  goods,  duty  30%. 

6.  $700  worth  of  goods,  duty  60%. 

7.  $500  worth  of  goods,  duty  35%. 

8.  $2000  worth  of  goods,  duty  45%. 

9.  $88.40  worth  of  goods,  duty  12j%. 

10.  $60.30  worth  of  goods,  duty  16f  %. 

11.  600  lb.  of  goods,  duty  22/  per  pound. 

12.  1100  lb.  of  goods,  duty  44/  per  pound. 

13.  6000  sq.  ft.  of  plate  glass,  duty  8/  per  square  foot. 


196    '  TAXES 

WRITTEN   EXERCISE 

1.  What  is  the  duty  on  $4350  worth  of  bronzes  at  45%? 
Is  this  specific  or  ad  valorem  ? 

2.  What  is  the  duty  on  3500  bu.  of  barley  at  30  ct.  per 
bushel  ?    Is  this  specific  or  ad  valorem  ? 

3.  What  is  the  duty  on  15  sets  of  Thackeray's  works 
at  £7  a  set,  allowing  $4.87  to  the  pound,  the  duty  being 

4.  What  is  the  duty  on  2  doz.  sets  of  Scott's  works  at 
£4  10s.  a  set,  allowing  $4.87  to  the  pound,  the  duty  being 
25%? 

5.  What  is  the  duty  on  2000  yd.  of  tapestry  Brussels^ 
27  in.  wide,  invoiced  at  $1.50  a  yard,  at  28  ct.  per  square 
yard  and  40%  ad  valorem  ? 

6.  What  is  the  duty  on  $3500  worth  of  ready-made 
clothing  at  50%  ad  valorem,  and  $1800  worth  of  silk 
dresses  at  60%  ad  valorem? 

7.  A  man  bought  a  painting  in  Eome,  paying  750  lire 
(francs)  for  it.  Allowing  19.3  ct.  to  the  lira,  what  did  it  cost 
in  our  money,  and  what  was  the  duty  at  25%  ?  What  was 
the  total  cost,  including  the  duty  ? 

8.  A  jeweler  bought  an  invoice  of  Swiss  watches,  paying 
9875  f r.  for  them  in  Geneva.  Allowing  19.3  ct.  to  the  franc, 
what  was  the  cost  in  our  money,  and  what  was  the  duty  at 
40%  ?    What  was  the  total  cost,  including  the  duty? 

9.  A  lady  traveling  in  Europe  bought  $650  worth  of 
jewelry  (duty  60%),  $250  worth  of  silk  dresses  (duty  60%), 
$75  worth  of  engravings  (duty  25%),  and  a  10  x  12  Oriental 
rug  costing  $700  (duty  10  ct.  per  square  foot  and  40%). 
What  duty  did  she  have  to  pay,  if  $100  worth  of  goods 
(jewelry  in  this  case)  was  admitted  duty  free? 


CUSTOMS  DUTIES  197 

190.  Table  of  customs  duties.    The   following  is  a  table 
of  certain  dutiable  articles  : 

Books  in  English     .     25%  Barley,  48  lb.  to  the  bu.    ^Of'  per  bu. 

Bronzes      ....     45%  Blankets       .     .      22^^  per  lb.  +  30% 

Cheese  ...      6)^  per  lb.  Flannel  cloth    .      22^  per  lb.  +  30% 

Cotton  handkerchiefs  45%  Fruits,  preserved  .  1^  per  lb.  +  35% 

Diamonds,  cut  and  set  60%  Glass,  plate       ...   8)^  per  sq.  ft. 

Hay  .     .     .     .    $4  per  ton  Knit  woolen      .     44j^  per  lb.  +  50% 

Paintings   ....     20%  Matches        ....    8/  per  gross 

Potatoes      .     .2of  per  bu.  Perfumery    .     .     QOj^  per  lb.  +  45% 

Watches     ....     40%  Soap,  toilet  ....       Ib^  per  lb. 

WRITTEN  EXERCISE 

Mnd  the  duty  on  the  following  : 

1.  A  $1500  diamond  necklace. 

2.  An  oil  painting  worth  $1250. 

3.  A  bronze  statue  costing  $2500. 

4.  A  car  load  of  barley  weighing  5  tons. 
6.    A  shipment  of  cheese  weighing  650  lb. 

6.  A  dozen  Swiss  watches  worth  $45  each. 

7.  An  English  encyclopedia  valued  at  $150. 

8.  A  case  of  matches  containing  1000  gross. 

9.  A  350-lb.  bale  of  flannel  cloth  worth  $400. 

10.  A  shipment  of  toilet  soap  weighing  500  lb. 

11.  A  150-lb.  box  of  knit  woolen  goods  valued  at  $425. 

12.  A  hundredweight  of  preserved  fruits  valued  at  $40. 

13.  Three  hundred  pieces  of  plate  glass,  each  16"  x  24". 

14.  Fifty  tons  of  hay  and  a  car  load  of  250  bu.  of  potatoes. 

15.  A  bale  of  blankets  weighing  225  lb.  and  worth  $300. 

16.  A  hundred  dozen  cotton  handkerchiefs  @  60/  a  dozen. 


198  TAXES 

191.  State  and  local  taxes.  State  and  local  taxes  are 
usually  a  certain  per  cent  levied  on  the  property  of  business 
concerns,  on  land,  on  money,  and  on  other  property. 

192.  Assessors.  The  property  to  be  taxed  is  valued  by 
oJSicers  called  assessors. 

193.  Assessed  valuation.  The  value  placed  upon  property 
for  taxation  is  called  the  assessed  valuation, 

194.  Rate  of  taxation.  Upon  the  assessed  valuation  a  cer- 
tain 7'ate  of  taxation  is  fixed. 

The  words  rate  of  taxation  are  often  used  to  designate 
the  number  of  mills  of  tax  on  each  dollar  of  valuation. 

Thus,  a  tax  of  5  J  mills  means  5 J  mills  on  a  dollar. 

Male  citizens  over  21  yr.  of  age  pay  a  poll  (head)  tax  in 
parts  of  the  country. 

This  is  a  fixed  sum,  usually  about  $1. 

195.  Illustrative  problem.  For  example,  if  a  village  with 
an  assessed  valuation  of  $3,200,-  ^^  ^^^^ 

000   must    raise    $16,800,    what       32OOO00)$i6800^ 
is  the  rate  of  taxation?  160000 

$16,800 -^  3,200,000  =  $0.005i.  8000    ^^=4 


ORAL  EXERCISE 

State  the  tax  on  the  following  amounts: 

1.  $1000  @  5  mills.  2.  $1000  @  4  mills. 

3.  $2000  @  6  mills.  4.  $5000  @  5  mills. 

5.  $5000  @  4  mills.  6.  $7500  @  4  mills. 

7.  $7000  @  5  mills.  8.  $1000  @  4|  mills. 

9.  $7500  @  6  mills.  10.  $2000  @  5^  mills. 

11.  $1000  @  3^  mills.  12.  $10,000  @  5|  mills. 


STATE  AND  LOCAL  TAXES  199 

WRITTEN  EXERCISE 

1.  What  is  the  tax  on  $6500  at  GJ  mills  on  a  dollar? 

2.  The  rate  of  taxation  being  1^%,  how  much  must  a 
company  pay  whose  property  is  assessed  at  $75,000  ? 

3.  A  town  has  an  assessed  valuation  of  $4,500,000,  and 
it  has  to  raise  $24,750  by  taxation.    What  is  the  rate  ? 

4.  The  rate  of  taxation  being  7^  mills,  how  much  tax 
must  a  man  pay  on  $8500,  together  with  $1  poll  tax? 

5.  A  town  has  an  assessed  valuation  of  $720,000,  and  it 
wishes  to  levy  a  tax  of  $5400  for  highways  and  schools. 
What  must  be  the  rate  ? 

6.  What  is  the  total  tax  of  a  man  whose  property''  is 
assessed  at  $8400,  the  rate  being  1  mill  for  state  purposes, 
3  mills  for  county  purposes,  ^  mill  for  the  town,  and  2 
mills  for  school  purposes,  together  with  $1  poll  tax? 

Griven  the  following  assessed  valuations  and  tax  levies^ 
find  the  rates  of  taxation : 

7.  $4,200,000,  $16,800.         8.    $2,900,000,  $8700. 
9.    $3,700,000,  $20,350.       10.   $7,875,000,  $23,625. 

11.    $9,250,000,  $41,625.       12.    $14,500,000,  $87,000. 

Given  the  following  tax  levies  and  rates  of  taxation, 
find  the  assessed  valuation : 

13.    $13,750,  5  mills.  14.    $21,000,  6  mills. 

15.    $57,750,  7  mills.  16.    $73,000,  8  mills. 

Given  the  following  assessed  valuations  and  rates,  find 
the  tax  levies: 

17.    $4,230,000,  4^  mills.       18.    $6,350,000,  7^  mills. 
19.    $7,250,000,  5i  mills.       20.    $12,780,000,  6J  mills. 


200 


TAXES 


196.  Tax  table.    Collectors  make  out  a  tax  table  like  this : 


Tax  Table. 

Rate 

5|  Mills  on 

$1 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0 

0000 

0055 

0110 

0165 

0220 

0275 

0330 

0385 

0440 

0495 

1 

0550 

0605 

0660 

0715 

0770 

0825 

0880 

0935 

0990 

1045 

2 

1100 

1155 

1210 

1265 

1320 

1375 

1430 

1485 

1540 

1595 

3 

1650 

1705 

1760 

1815 

1870 

1925 

1980 

2035 

2090 

2145 

4 

2200 

2255 

2310 

2365 

2420 

2475 

2530 

2585 

2640 

2695 

5 

2750 

2805 

2860 

2915 

2970 

3025' 

3080 

3135 

3190 

3245 

6 

3300 

3355 

3410 

3465 

3520 

3575 

3630 

3685 

3740 

3795 

7 

3850 

3905 

3960 

4015 

4070 

4125 

4180 

4235 

4290 

4345 

8 

4400 

4455 

4510 

4565 

4620 

4675 

4730 

4785 

4840 

4895 

9 

4950 

5005 

5060 

5115 

5170 

5225 

5280 

5335 

5390 

5445 

Here  the  first  figure  of  the  number  of  dollars  assessed  is 
given  at  the  left,  and  the  second  one  at  the  top.  Thus,  at 
h\  mills  on  $1,  the  tax  on  $100  is  $0.55  ;  on  $250,  $1.37^. 

197.  Collector's  commission.  The  law  allows  the  collector 
a  commission  on  the  tax  collected,  usually  about  1%. 

198.  Illustrative  problem.  What  must  a  man  pay  on  $8250, 
at  h\  mills  on  $1,  the  collector's  commission  being  1%? 

By  the  table,  the  tax  on  $8200  is  $45.10 

"      "     "  50  "       0,28  (really  Ti\f) 

"      "     ''  $8250  "  ^45.38 

Add  collector's  1%  on  the  tax  .46  (really  45.38^) 


$45.84 


WRITTEN   EXERCISE 

Find  the  tax  at  b\  mills^  as  in  §  198: 
1.    $6500.  2.    $8750.  3.    $4875. 

5.    $12,000.        6.    $16,500.        7.    $24,400. 


4.    $7675. 
8.    $23,500. 


9.    $31,100.      10.    $23,250.      11.    $18,875.     12.    $45,250. 


FIRE  INSURANCE  201 

FIRE   INSURANCE 

199.  Insurance.  An  agreement  to  compensate  any  one  for 
some  specified  loss  is  called  insurance, 

200.  Policy.  The  written  agreement  of  an  insurance  com- 
pany to  pay  a  certain  amount  in  case  of  loss  is  called  db  policy. 
The  insurance  companies  are  often  called  underwriters. 

201.  Face  of  policy.  The  amount  specified  to  be  paid  in 
case  of  loss  is  called  the  face  of  the  policy. 

202.  Premium.  The  cost  of  insurance  is  called  the  pre- 
mium. The  rate  of  prewAum.  is  sometimes  stated  as  a  certain 
sum  for  each  $100,  and  sometimes  as  a  certain  rate  per  cent. 

Houses  are  usually  insured  for  three  or  five  years,  busi- 
ness property  is  usually  insured  for  one. 

203.  Illustrative  problem.  What  is  the  premium  for  insur- 
ing a  store  against  loss  by  fire,  for  $4000  at  $1.20  a  year? 

1.  Since  the  rate  is  $1.20  on  $100,  it  is  $0,012  on  $1. 

2.  4000  times  $0,012  equals  $48,  the  premium.    . 

ORAL  EXERCISE 

1.  What  is  the  premium  on  a  $650  policy  at  2%  ? 

2.  What  is  the  premium  on  a  $3000  policy  at  1J%  ? 

3.  A  farmer  insured  his  growing  crop  of  wheat  for  $800 
at  4%.    What  was  the  premium ? 

4.  A  building  which  cost  $24,000  is  insured  for  |  of  its 
cost.    What  is  the  face  of  the  policy? 

5.  A  man  paid  $20  for  insuring  his  house,  the  rate  being 
1%.    What  was  the  face  of  the  policy  ? 

6.  A  schoolhouse  is  insured  at  1%,  the  premium  being 
$50.  The  face  of  the  policy  is  f  of  the  value  of  the  build- 
ing.   Eequired  the  value. 


202  FIRE  INSURANCE 

State  the  premiums  on  the  following  policies  at  the  rates 
specified : 

7.  $1000,11%.  8.  $725,4%. 

9.  $2000,  lt%.  10.  $825,4%. 

11.  $2000,  2^%.  12.  $500,  2^%. 

13.  $3000,  1J%.  14.  $700,  2^%. 

15.  $4000,  2f  %.  16.  $900,  11%. 

17.  $2500,  11%.  18.  $650,  11%. 

19.  $3500,  1.2%.  20.  $1250,  4%. 

21.  $4250,  $2.  22.  $6250,  $2. 

23.  $1750,  $2.  24.  $3750,  $2. 

25.  $12,500,  $1.  26.  $12,000,  $3. 

27.  $25,000,  $3.  28.  $15,000,  $2. 

29.  $10,000,  $1.75.  30.  $50,000,  $1.50. 

State  the  faces  of  the  policies^  given  the  following  pre- 
miums and  rates: 

31.    $70,  2%.  32.    $90,  2%. 

33.    $17,  i%.  34.    $50,  2i%. 

35.    $25,  2i%.  36.    $13.75,  1%. 

37.    $17.50,  1%.  38.    $18.50,  i%. 

State  the  rates^  given  the  following  faces  of  policies  and 
premiums  : 

39.    $1500,  $15.  40.    $2000,  $10. 

41.    $2500,  $50.  42.    $3500,  $35. 

43.    $5000,  $25.  44.    $7500,  $150. 

45.    $6000,  $60.  46.    $6500,  $130. 

47.    A  building  worth  $8000  is  insured  for  |  of  its  value 
at  1%.    What  is  the  premium? 


FIRE  INSURANCE  203 

WRITTEN  EXERCISE 

1.  At  $0.95,  what  is  the  premium  on  a  $2500  policy? 

2.  At  $1.10,  what  is  the  premium  on  a  $2800  policy? 

3.  At  $1.15,  what  is  the  premium  on  a  $3750  policy? 

4.  A  building  worth  $12,000  is  insured  for  f  of  its  value 
at  2  % .    What  is  the  premium  ? 

5.  If  you  insure  the  contents  of  your  store  for  $6000, 
what  is  the  premium,  at  $1.25? 

6.  The  premium  for  insuring  some  property  at  $1.50 
is  $52.50.    What  is  the  face  of  the  policy? 

7.  A  man  insured  his  factory,  valued  at  $135,000,  for 
J  of  its  value,  at  $1.90.    What  was  the  premium? 

.  8.  A  dealer  insured  his  stock  of  goods,  valued  at  $14,000, 
for  I  of  its  value,  at  $1.65.    What  was  the  premium  ? 

9.    If  a  3-year  policy  for  $1750  costs  $27,  what  is  the 
rate  of  premium  for  the  3  years  ?    What  is  the  rate  per  year  ? 

10.  If  a  3-year  policy  for  $3000  costs  $36,  what  is  the  rate 
of  premium  for  the  3  years?    What  is  the  rate  per  year? 

11.  A  merchant  insured  his  stock  for  |  of  its  value,  at 
1|<^.  The  premium  was  $131.25.  What  was  the  value  of 
the  stock? 

12.  A  manufacturer  insured  his  factory  for  |  of  its  value, 
at  $2.  The  premium  was  $210.  What  was  the  face  of  the 
policy?  the  value  of  the  factory? 

13.  A  factory  worth  $33,000  is  insured  for  |  of  its  value, 
at  2%.  In  case  of  total  loss  how  much  would  the  owner 
lose,  including  his  premium  paid? 

14.  A  man  insured  his  library  for  its  full  value,  $2500, 
at  $1.25.  What  was  the  premium?  If  a  fire  destroyed  f 
of  the  library,  how  much  could  he  recover? 


204  FIRE  INSURANCE 

15.  Which  is  the  cheaper,  a  3-year  policy  on  $3500  at 
1^%,  or  an  annual  policy  renewed  for  the  same  period,  at 
60/  a  year  ?    How  much  cheaper  ? 

\l6.  If  Mr.  Wood  insures  his  stock  of  goods,  invoiced  at 
$28,000,  for  80%  of  its  value,  at  li%,  and  the  property  is 
entirely  destroyed  by  fire,  what  is  his  loss,  including  the 
premium  paid? 

Include  the  premium  in  Exs.  17,  18. 

17.  A  dealer  insured  his  stock  of  goods,  valued  at  $21,800, 
for  I  of  its  value,  at  1.3%.  The  property  was  entirely 
destroyed  by  fire.    What  was  his  loss  ? 

18.  If  Mr.  Baldwin  insures  his  stock  of  goods,  invoiced 
at  $37,500,  for  80%  of  its  value,  at  95/,  and  the  property 
is  entirely  destroyed  by  fire,  what  is  his  loss  ? 

\  19.  Suppose  a  company  willing  to  take  a  risk  covering 
the  value  of  a  stock  of  goods  and  the  premium  paid,  and 
the  face  of  the  policy  is  $25,500,  the  rate  being  2%,  what 
is  the  value  of  the  stock  of  goods  ? 

20.  A  dealer  pays  $21  premium  for  insuring  a  shipment 
of  grain  at  1|%.  What  is  the  face  of  the  policy?  When 
this  grain  is  placed  in  the  elevator  it  is  again  insured  for 
the  same  amount  at  i%.    What  is  the  premium? 

V.  21.  A  manufacturer  of  especially  inflammable  goods 
finds  that  the  insurance  rate  is  6%  a  year.  Rather  than 
pay  such  a  rate,  he  could  afford  to  have  his  stock  burn 
once  in  how  many  years,  not  counting  interest? 

22.  If  Roberts  &  Eastman  insure  their  business  block 
for  $12,000,  at  $1.15 ;  the  first-floor  contents  for  $8000,  at 
$1.25  (on  account  of  the  difficulty  of  removing  goods);  and 
the  contents  of  the  other  floors  for  $3000,  at  $1.40,  what 
is  the  total  amount  of  premiums  paid  ? 


MARINE  INSURANCE  206 

MARINE   INSURANCE 

204.  Marine  insurance.  Insurance  against  loss  by  naviga- 
tion is  called  marine  insurance. 

The  value  placed  on  the  goods  is  the  same  as  the  face  of  the 
policy  unless  the  contrary  is  stated. 

WRITTEN  EXERCISE 

1.  A  man  paid  $36  for  insuring  some  goods  from  Phila- 
delphia to  Marseilles,  the  rate  being  J%,  less  20%  of  the 
premium.    What  was  the  face  of  the  policy? 

2.  A  new  ocean-going  tug  running  between  Norfolk,  Va., 
and  Eastport,  Me.,  is  insured  at  5%  a  year,  the  premium 
being  $2245.    What  is  the  face  of  the  policy? 

3.  A  man  pays  $24,793.35  for  a  cargo  of  hides  in 
Galveston,  which  included  the  premium  at  ^%  net  for 
shipping  the  same  to  New  York.  What  was  the  amount 
of  premium? 

4.  What  is  the  premium  on  a  shipment  of  $10,200  worth, 
of  boots  and  shoes  by  steamer  from  New  York  to  Manila, 
the  rate  being  1^%,  less  20%  (see  Ex.  1)?  How  much  is 
it  by  sailing  vessel,  the  rate  being  2%,  less  20%  ? 

5.  What  is  the  premium  on  an  under-deck  shipment  of 
$9000  worth  of  lumber  from  Georgia  to  New  York,  the 
rate  being  |%,  less  20%  ?  What  is  it  for  a  shipment  made 
on  deck,  the  rate  being  2^%,  less  20%?  How  much  pre- 
mium is  saved  by  taking  the  under-deck  shipment? 

6.  What  is  the  premium  on  a  shipment  of  $8460  worth 
of  typewriters  by  passenger  steamer  from  New  York  to 
Liverpool,  the  rate  being  0.2%  net?  How  much  by  a 
tramp  steamer,  the  rate  being  |%,  less  20%?  How  much 
by  a  sailing  vessel,  the  rate  being  1^-%,  less  20%? 


206  LIFE  INSURANCE 

LIFE   INSURANCE 

205.  Why  a  man  should  insure  his  life.  If  a  man  is  careful 
as  to  the  future  and  considers  the  fact  that  in  later  years 
there  will  probably  be  one  or  more  persons  dependent  upon 
him,  he  will  wish  to  insure  his  life.  The  earlier  this  is  done 
the  lower  will  be  the  premium  and  the  sooner  he  will  cease  to 
make  payments  if  he  takes  a  10-,  15-,  or  20-payment  policy. 

Premiums  are  stated  at  so  much  on  $1000.  They  vary 
with  the  age,  being  smaller  for  young  persons. 

The  best  plan  is  to  take  a  policy  in  a  company  of  unquestion- 
able standing,  and  never  forfeit  it  by  nonpayment  of  premiums. 

ORAL   EXERCISE 

State  the  premiums  on  the  following  policies^  the  premium 
on  $1000  being  given: 

1.    $15,000,  %2Q,  2.  $3500,  $25. 

3.    $2000,  $21.30.  4.  $4500,  $30. 

5.    $3000,  $22.10.  6.  $5500,  $30. 

7.    $4000,  $22.50.  8.  $12,000,  %2B. 

9.    $5000,  $28.40.  10.  $2500,  $22.20. 

11.    $10,000,  $27.65.  12.  $20,000,  $31.20. 

State  the  faces  of  the  policies^  given  the  following  pre- 
miums and  the  premiums  on  $1000 : 

13.    $131,  $26.20.  14.    $175,  $25. 

15.    $54.20,  $27.10.  16.    $49,  $24.50. 

17.    $96.60,  $32.20.  18.    $63.90,  $21.30. 

State  the  premiums  on  $1000^  given  the  following  polir 
cies  and  premiums : 

19.    $3000,  $84.  20.    $4000,  $27. 


KINDS  OF  POLICIES  207 

206.  Kinds  of  policies.  Four  of  the  leading  kinds  of 
policies  are: 

1.  Ordinary  life,  the  insured  agreeing  to  pay  a  certain 
premium,  usually  annually,  for  life. 

The  rate  is  always  given  as  the  cost  of  $1000  worth  of  insurance. 
That  is,  the  rate  $25.50  means  that  the  annual  premium  on  a 
policy  for  $1000  is  $25.50.  Some  insurance  companies  allow 
dividends  each  year,  thus  reducing  the  premium  slightly. 

2.  Limited  life,  the  premiums  being  payable  for  some 
fixed  number  of  years,  as  twenty,  the  policy  then  being 
called  paid  up  (no  more  premiums  being  due),  but  the  face 
not  being  paid  until  the  death  of  the  insured. 

Naturally  the  premiums  are  higher  on  this  form. 

3.  Endowment,  the  premiums  being  paid  for  some  fixed 
number  of  years,  as  ten,  fifteen,  or  twenty,  at  the  end  of 
which  time  the  face  of  the  policy  will  be  paid  to  the  insured. 

Since  this  may  be  paid  during  the  lifetime  of  the  insured,  the 
premiums  are  also  higher  than  on  an  ordinary  life  policy. 

4.  Term  insurance,  the  premiums  being  paid  for  a  speci- 
fied length  of  time  and  the  face  of  the  policy  being  pay- 
able if  the  insured  dies  within  the  term  of  insurance. 

Thus,  a  person  may  insure  his  life  or  his  health  for  thirty 
days,  as  in  certain  forms  of  accident  insurance.  He  may  also 
insure  his  life  for  a  certain  number  of  years  only.  The  premium 
on  this  form  of  policy  is  low,  since  the  company  may  not  have 
to  pay  the  face  at  all. 

There  are  various  other  forms  of  policy,  but  most  of 
them  are  modifications  of  the  above  types.  Some  are 
arranged  so  that  the  face  will  not  be  paid  on  the  death  of 
the  insured,  but  a  certain  amount  will  be  paid  annually 
(an  annuity)  during  the  lifetime  of  the  one  for  whose 
benefit  the  policy  was  written. 


208  LIFE  INSURANCE 


WRITTEN   EXERCISE 


1.  What  is  the  premium  on  a  $5000  policy  at  $27.39 
on  $1000? 

2.  What  annual  premium  must  a  man  pay  on  a  10-year 
endowment  policy  for  $4000  at  $102.60  per  thousand? 
What  would  he  pay  in  the  10  years? 

3.  If  a  young  man  takes  out  a  $5000  20-payment  policy 
at  $27.39  per  thousand,  how  much  will  he  have  paid  when 
the  policy  matures  (that  is,  after  20  payments)  ? 

4.  What  is  the  premium  on  a  $5000  20-payment  policy 
of  such  a  kind  that  the  rate  is  $34.20  on  a  thousand? 
What  are  the  total  premiums  for  the  20  years  ? 

6.  What  is  the  premium  on  a  $7500  20-payment  policy 
of  such  a  kind  that  the  rate  is  $32.50  on  a  thousand? 
What  are  the  total  premiums  for  the  20  years? 

6.  If  a  man  takes  out  a  $2500  policy  in  one  company 
at  $26.40  per  thousand,  and  a  $3500  policy  in  another  at 
$23.50  per  thousand,  what  are  his  annual  premiums? 

7.  A  young  man  takes  out  a  $10,000  policy  on  the  25- 
payment  plan,  at  $26.36  per  thousand.  What  is  the  annual 
premium  ?    How  much  are  the  premiums  for  the  25  years  ? 

8.  A  man  takes  out  a  $5000  policy,  paying  $26.40  a 
thousand.  He  dies  just  before  the  eighth  annual  payment 
is  due.  How  much  does  his  estate  receive  above  what  he 
paid  to  the  company  ? 

9.  A  young  man  took  out  a  $5000  20-payment  policy 
20  years  ago,  paying  $136.95  a  year.  How  much  has  he 
paid  in  the  20  years  ?  Estimating  that  the  insurance  com- 
pany has  had  the  use  of  all  this  amount  for  the  equivalent 
of  10  years,  at  4%,  what  is  the  total  amount  received  by 
the  company? 


LIFE  INSURANCE  209 

10.  A  man  pays  $61.50  annually  on  a  $2500  policy. 
What  is  the  rate  of  premium  per  thousand  dollars  ? 

11.  At  the  age  of  21  the  annual  premium  on  $1000  of 
term  insurance  for  10  years  is  $11,  and  the  dividends 
decrease  each  premium,  after  the  first,  15%  of  this  sum. 
What  is  the  total  net  cost  of  $10,000  of  such  insurance  for 
10  years  ? 

12.  At  the  age  of  21  the  annual  premium  on  an  ordinary 
life  policy  is  $19.12  per  thousand.  What  would  be  the 
total  amount  of  premiums  paid  on  $5000  in  20  years? 
What  would  be  the  net  amount  if  the  company  allowed 
$198  per  thousand  in  dividends  during  this  period? 

13.  How  much  more  would  the  policy  of  Ex.  12  cost  if 
taken  out  at  the  age  of  32,  the  premium  then  being  $25.09, 
and  the  dividends  for  20  years  being  $237  per  thousand? 

14.  At  the  age  of  21  the  annual  premium  on  a  20-payment 
limited  life  policy  is  $28.98,  and  the  dividends  allowed  by 
a  certain  company  amount  to  $222  per  thousand  in  20 
years.  What  is  the  net  cost  of  $3000  of  such  insurance 
before  it  is  paid  up  ? 

Of  course  the  insured  also  loses  the  interest  on  the  premiums 
paid,  but  this  item  is  not  required  in  the  example. 

15.  How  much  more  would  the  policy  of  Ex.  14  cost  if 
taken  out  at  the  age  of  50,  the  premium  then  being  $54.65, 
and  the  total  amount  of  the  dividends  for  20  years  being 
$625  per  thousand? 

16.  At  the  age  of  21  the  annual  premium  on  a  20-year 
endowment  policy  is  $48.48,  and  the  dividends  amount  to 
$353  per  thousand  during  this  period.  What  is  the  differ- 
ence between  the  amount  paid  the  company  (less  dividends) 
and  the  amount  received  in  return  on  a  $5000  policy? 


210  CORPORATIONS 

II.   BUSINESS  ARITHMETIC  COMPLETED.    MENSURATION 
CORPORATIONS 

207.  Corporation.  The  laws  of  our  various  states  permit 
a  number  of  persons  who  wish  to  go  into  business  together 
to  organize  as  one  body,  called  a  corporation, 

208.  Capital.  The  members  contribute  the  money  to  start 
the  business.    This  is  called  the  capital. 

209.  Shares  of  stock.  The  capital  is  divided  into  shares, 
usually  of  $100  each,  although  sometimes  less.  Each  person 
who  owns  one  or  more  shares  is  a  stockholder^  and  receives  a 
certificate  of  stock  stating  how  many  shares  he  owns. 

For  example,  if  the  capital  is  $100,000,  and  the  shares  are  $100 
each,  there  are  1000  shares.  If  a  man  has  50  shares,  he  owns 
$5000  worth  of  stock,  or  5%  of  the  whole  corporation. 

210.  Directors  and  officers.  The  stockholders  elect  a  few 
of  their  number  to  have  general  direction  of  the  company. 
These  are  called  directors,  and  they  elect  the  officers. 

211.  Dividends.  The  earnings  of  the  company,  after  pay- 
ing the  expenses  and  providing  for  a  bank  account  suffi- 
cient for  probable  needs,  are  divided  into  dividends,  the 
directors  deciding  on  the  rate  of  dividend.  These  dividends 
are  sent  to  the  stockholders,  by  means  of  checks. 

For  example,  if  a  company  with  a  capital  of  $100,000  earns 
$6000  beyond  all  expenses,  it  may  declare  a  6%  dividend.  Then  a 
man  who  owns  $5000  worth  of  stock  will  receive  a  check  for  $300. 

ORAL  EXERCISE 

State  the  dividends  to  he  paid  on  the  following : 

1.    $3000,  5%.     2.    $7000,  4%.       3.    $12,000,  5^%. 

4.    $2500,3%.     5.    $8000,11%.     6.    $20,000,  2^%. 


CORPORATIONS  211 


WRITTEN  EXERCISE 


1.  How  many  shares  in  a  company  with  $1,500,000 
capital?    (In  these  exercises  let  one  share  be  $100.) 

2.  A  company  divides  $50,000  in  dividends,  and  stock- 
holders receive  $4  per  share.    What  is  the  capital? 

3.  A  company  with  $3,000,000  capital  declares  a  5% 
dividend.    What  does  the  holder  of  100  shares  receive? 

4.  A  company  with  $500,000  capital  divides  $45,000  in 
dividends.    What  does  the  holder  of  30  shares  receive? 

5.  How  much  does  the  holder  of  30  shares  of  a  certain 
railway  stock  receive  when  a  4-i-%  dividend  is  declared? 

6.  A  man  receives  from  the  treasurer  of  a  certain  com- 
pany $25  every  three  months,  as  dividends  on  his  20  shares 
of  stock.    What  is  the  rate  of  quarterly  dividends  ? 

7.  A  company  with  a  capital  of  50  million  dollars 
declares  a  dividend  of  2j%  every  six  months.  How  much 
money  does  it  distribute  among  its  stockholders  annually? 

8.  A  company  with  $250,000  capital  declares  four  divi- 
dends a  year,  each  of  1:|%.  What  are  the  total  annual 
dividends?  What  is  the  annual  income  of  a  man  who  owns 
50  shares? 

9.  A  company  with  $350,000  capital  declares  two  divi- 
dends a  year.  A  stockholder  who  owns  20  shares  receives 
an  annual  income  of  $110.  What  is  the  rate  of  the  semi- 
annual dividends? 

10.  A  company  with  a  capital  of  $250,000  has  earned 
$15,000  this  year  above  all  expenses.  It  decides  to  save 
$2500  of  this  for  emergencies,  and  to  divide  the  rest  in 
dividends.    What  is  the  rate? 


212  CORPORATIONS 

212.  Above  and  below  par.  If  stock  is  paying  a  high  rate 
of  dividend,  that  is,  more  than  can  be  received  from  good 
ordinary  investments,  people  will  be  so  anxious  to  buy  it 
that  they  will  pay  more  than  $100  for  a  $100  share.  It 
is  then  said  to  be  above  par.  If  a  $100  share  can  be  bought 
for  just  $100,  the  dividends  are  about  on  a  par  with  other 
investments,  and  the  stock  is  said  to  be  at  par.  If  the 
dividends  are  low,  say  1%  or  2^,  people  will  not  be  anxious 
to  buy  the  stock,  and  it  will  sell  below  par. 

213.  Buying  stock.  Stocks  are  usually  bought  and  sold 
through  a  broker,  generally  at  a  stock  .exchange,  a  kind  of 
auction  room  for  such  business. 

214.  Brokerage.  The  broker  charges  brokerage  or  commis- 
sion, usually  \(^o  of  the  par  value,  making. this  charge  both 
for  buying  and  for  selling. 

215.  Meaning  of  stock  quotations.  A  quotation  of  118j 
means  that  $100  worth  of  stock  will  cost  $118.75  besides 
$i  (or  12^  ct.)  brokerage.  The  buyer  then  pays  $118.87^ 
per  share,  while  the  seller,  who  must  also  pay  his  broker, 
receives  $118.75  -  $0.12^  =  $118,621  per  share. 

In  stock  quotations  fractions  are  always  expressed  in  halves, 
fourths,  or  eighths.  Fractions  of  a  share  cannot  be  bought  on 
the  stock  exchange.  The  standard  amount  bought  is  100  shares, 
although  smaller  lots  are  often  purchased. 

216.  Illustrative  problems.  1.  What  is  the  cost  of  10 
shares  of  stock  quoted  at  137^,  brokerage  as  usual? 

One  share  costs  $137^  +  $i  brokerage,  or  $137^. 
10  shares  cost  10  times  $137J,  or  $1372.50. 

2.  What  is  the  amount  received  from  the  sale  of  100 
shares  of  stock  quoted  at  96|,  allowing  the  usual  brokerage  ? 
One  share  brings  $96f  —  ^\  brokerage,  or  $96^. 
100  shares  bring  100  times  $96 J,  or  $9650. 


BUYING  STOCK  213 

ORAL  EXERCISE 

State  the  cost  of  10  shares  of  stock  quoted  as  follows^ 
adding  the  brokerage  in  each  ease : 

1.    94|.  2.    l^.  3.    69f.  4.    84|. 

5.    114J.  6.    63|.  7.    47|.  8.    82f 

9.    106|.  10.    127|.  11.    75f.  12.    109  J. 

State  the  amount  received  from  the  sale  of  10  shares 
of  stock  quoted  as  follows^  allowing  for  the  brokerage  : 
13.    871.  14.   691.  15.   541.  16.   96|. 

17.    134f  18.    68|.  19.    72|.  20.    107^. 

State  the  cost  of  the  following^  including  brokerage  : 
21.    100  shares  @  47|.  22.    100  shares  @  347. 

23.    50  shares  @  119J.  24.    50  shares  @  123J. 

WRITTEN   EXERCISE 

jFmc?  the  cost  of  the  following,  including  brokerage  : 

1.    75  shares  @  127i.  2.    25  shares  @  136 J. 

3.    60  shares  @  141|.  4.    125  shares  @  62|. 

5.    150  shares  @  109i.  6.    250  shares  @  172J. 

jPmc?  ^Ae  amount  received  from  the  sale  of  the  following: 
7.    80  "shares  @  134i.  8.    500  shares  @  64. 

9.    175  shares  @  169.  10.    250  shares  @  178. 

11.    140  shares  @  147f .  12.    120  shares  @  142^. 

13.  A  man  paid,  including  brokerage,  $2047.50  for  30 
shares  of  stock.     At  what  price  was  it  quoted  ? 

14.  A  man  received  for  some  stock,  less  the  brokerage, 
$5195,  when  it  was  quoted  at  130.    How  much  did  he  sell? 


214  CORPORATIONS 

217.  Newspaper  quotations.  Daily  newspapers  give  the 
stock  quotations.  The  following  examples  may  be  solved 
by  using  the  newspaper  quotations,  or  the  following : 


At.,  Top.  &  S.  F. 

85  J 

N.  Y.  Central 

138J 

Bait.  &  Ohio 

95} 

Penn.  R.R. 

139i 

Can.  Pac. 

130i 

Southern  Pac. 

62f 

111.  Cent. 

1521 

Union  Pac. 

113i 

Louisv.  &  Nash. 

132f 

Western  Un.  Tel. 

93 

Missouri  Pac. 

1011 

Wisconsin  Cent. 

20 

$115f 
113^ 

^2i 
10 

In  the  following  examples  add  }%  to  the  quotation  if  you  are 
buying,  and  subtract  \%  if  you  are  selling,  to  pay  the  broker. 

218.  Illustrative  problem.  If  a  man  buys  10  shares  of 
Union  Pacific  when  quoted  at  113i  and  sells  it  when 
quoted  at  115f ,  how  much  does  he  gain  ? 

1.  He  buys  it  at  113 J  +  \  (brokerage),  or  113|. 

2.  He  sells  it  at  115}  —  }  (brokerage),  or  115f. 

3.  Therefore  he  gains  2|,  or  $2.25  a  share. 

4.  On  10  shares  he  gains  10  times  $2.25,  or  $22.50.  ^22.50 

WRITTEN   EXERCISE 

1.  A  man  buys  50  shares  of  Atchison,  Topeka  &  Santa  Fe 
stock  as  quoted,  and  sells  at  89 J.    What  is  his  gain? 

2.  A  man  bought  50  shares  of  Wisconsin  Central  when 
it  was  quoted  at  2 5 J,  and  sold  it  at  the  above  quotation. 
How  much  did  he  lose  ? 

3.  If  we  buy  20  shares  of  Baltimore  &  Ohio  at  90,  and 
100  shares  of  Canadian  Pacific  at  131,  and  sell  at  the 
above  quotations,  what  do  we  gain  or  lose  ? 

4.  Find  the  cost  of  50  shares  of  Pennsylvania  E.E.,  100 
shares  of  Southern  Pacific,  20  shares  of  Union  Pacific,  and 
10  shares  of  Western  Union  Telegraph  Co. 


BUYING  STOCK  215 

Find  the  gain  or  loss  on  buying  50  shares  of  the  following 
stocks  as  quoted  on  the  preceding  page,  and  selling  at  the 
prices  here  given : 

5.    111.  Cent.  153.  6.    111.  Cent.  149|. 

7,    Can.  Pac.  125.  8.   Union  Pac.  115. 

9.    Can.  Pac.  130^.  10.    Penn.  E.R.  137^. 

11.    Southern  Pac.  63^.  12.    Union  Pac.  114 J. 

13.    K  Y.  Central  136i.  14.   Penn.  KR.  139|. 

15.    At.,  Top.  &  S.F.  861  16.   Bait.  &  Ohio  97^. 

17.    Louisv.  &  Nash.  134.  18.    Missouri  Pac.  100^. 

19.  Western Un.  Tel.  87^.  20.   Wisconsin  Cent.  18j. 

21.  A  man  bought  40  shares  of  stock  and  sold  it  when 
quoted  at  127^.  He  gained  $80  on  the  deal.  What  was 
the  quoted  price  when  he  bought  it  ? 

22.  A  man  bought  150  shares  of  New  York  Central  stock 
when  quoted  as  on  page  214.  He  sold  it  so  as  to  gain  $600. 
What  was  the  quoted  price  when  he  sold  it? 

23.  If  a  dealer  buys  100  shares  of  Illinois  Central,  50 
shares  of  Louisville  &  Nashville,  and  25  shares  of  Missouri 
Pacific  at  the  quotations  on  page  214,  what  does  it  all  cost  ? 

24.  A  man  bought  some  Illinois  Central  stock  when 
quoted  as  on  page  214.  He  sold  it  when  quoted  at  150|,  and 
lost  $500  by  so  doing.    How  many  shares  did  he  buy? 

25.  A  man  bought  some  Canadian  Pacific  stock  when 
quoted  as  on  page  214.  He  sold  it  when  quoted  at  132^,  and 
madQ  $400  by  so  doing.    How  many  shares  did  he  buy  ? 

26.  A  man  buys  100  shares  of  New  York  Central  as 
quoted  on  page  214,  holds  it  a  year,  receives  5%  in  divi- 
dends (5%  on  the  par  value),  and  sells  it  at  141^.  Money 
being  worth  4%  a  year,  what  does  he  gain? 


216  CORPORATIONS 

219.  Bonds.  When  corporations  wish  to  borrow  any  con- 
siderable amount  of  money  they  issue  bonds. 

A  written  or  printed  promise  to  pay  a  certain  sum  at  a 
specified  time,  signed  by  the  maket  and  bearing  his  seal, 
is  called  a  bond. 

220.  Bonds  secured  by  a  mortgage.  Bonds  are  secured  by 
a  mortgage,  an  agreement  that  the  owners  of  the  bonds  may 
sell  the  property  if  the  bonds  and  the  interest  are  not  paid. 

221.  Difference  between  stocks  and  bonds.  Bonds  differ 
from  stocks  in  this  way :  the  stockholders  of  a  railway 
are  the  owners ;  the  bondholders  are  the  ones  to  whom 
the  road  owes  money.  Bonds  bear  a  fixed  rate  of  interest, 
but  the  income  of  stocks  depends  on  the  earnings  of  the 
company  after  the  interest  on  the  bonds  and  the  running 
expenses  have  been  paid. 

222.  Computing  dividends.  Stock  dividends  and  bond  in- 
comes are  always  computed  on  the  par  value. 

223„  Illustrative  problems.  1.  How  much  is  the  income 
on  $5000  worth  of  4%  bonds? 

4%  of  $5000  =  $200. 
2o  What  is  the  income  on  50  shares  of  railway  stock  at 

1.  50  shares  have  a  par  value  of  $5000. 

2.  5%  of  $5000  =  $250. 

3.  If  I  buy  a  5%  bond  at  124^,  what  is  the  rate  of 
income  on  my  investment? 

1.  I  pay  $124|  +  $i  (brokerage)  =  $125  for  a  $100  bond. 

2.  My  income  is  5%  of  $100,  or  $5. 

3.  Since  x%  of  $125  =  $5, 

therefore  x%  =  $5  ^  $125  =  .04. 

4.  Hence  my  income  is  4%  on  my  investment  (but  5%  on  the 
par  value),  not  considering  the  date  of  maturity. 


STOCKS  AND  BONDS  217 


WRITTEN   EXERCISE 


1.  What  will  75  shares  of  stock  cost  when  quoted  at  96^  ? 
at  102|?  at  6S^?  at  99f  ?    (Eemember  the  ^%.) 

2.  I  buy  a  6%  bond  at  149 J.  What  is  the  rate  of  income 
on  the  money  invested?    (Eemember  the  -^%.) 

3.  Which  gives  the  better  income,  5%  stock  bought 
when  quoted  at  139^  or  3J%  bonds  bought  when  quoted 
at  99 J? 

$5  --  $140,  compared  with  $3.50  -4-  $100. 

4.  Which  gives  the  better  rate  of  income,  a  6%  bond  at 
120  or  a  5%  promissory  note,  leaving  out  the  question  of 
brokerage  in  this  example? 

$6  -^  $120,  compared  with  $5  on  $100. 

6.  A  man  buys  some  stock  that  regularly  pays  7%  divi- 
dends, when  quoted  at  199|.  What  is  the  rate  of  income 
on  the  money  invested? 

6.  When  United  States  4%  bonds  are  quoted  at  116 J, 
what  rate  of  income  does  a  purchaser  receive  on  his  invest- 
ment, not  considering  the  question  of  the  date  of  maturity 
of  the  bonds  ? 

7.  If  you  had  some  money  to  invest,  which  would  you 
prefer,  a  stock  that  regularly  pays  8%,  quoted  at  159|,  a 
5%  bond  at  109|,  or  a  5^%  promissory  note,  the  security 
being  equally  good? 

Compare  $8  return  on  $160  invested,  $5  return  on  $110  invested, 
and  $5.50  return  on  $100  invested.  The  $8  on  $160  gives  an 
income  of  jf^  or  5%.    What  per  cent  do  the  others  give? 

8.  If  you  had  some  money  to  invest,  which  would  you 
prefer,  a  stock  that  regularly  pays  7%,  quoted  at  149|,  a 
4%  bond  at  89f,  or  a  4^%  promissory  note,  the  security 
being  equally  good? 


218  CORPORATIONS 

Find  which  pays   the  better  per  cent^  and  how  muchy 
not  considering  the  brokerage^  in  Exs,  9—21: 
9,    A  5%  bond  at  121,  or  a  4%  bond  at  97. 

10.  A  5%  bond  at  115,  or  a  4%  bond  at  92. 

11.  A  5%  bond  at  130,  or  a  6%  bond  at  156. 

12.  A  3%  bond  at  102,  or  a  5%  bond  at  170. 

13.  A  6%  bond  at  130,  or  a  5%  bond  at  108. 

14.  A  6%  bond  at  140,  or  a  5%  bond  at  117. 

15.  A  3%  bond  at  92,  or  a  3^^%  bond  at  107. 

16.  A  4^%  bond  at  par,  or  a  5%  bond  at  111. 

17.  A  5%  bond  at  20  above  par,  or  a  4%  bond  at  4 
below  par. 

This  means  a  5%  bond  at  120,  or  a  4%  bond  at  96. 

18.  A  6%  bond  at  30  above  par,  or  a  4%  bond  at  14 
below  par. 

19.  A  5%  bond  at  10  above  par,  or  a  4%  bond  at  12 
below  par. 

20.  A  stock  paying  regularly  7%,  at  140,  or  one  paying 
regularly  5%,  at  95. 

21.  A  stock  paying  regularly  6%,  at  137,  or  one  paying 
regularly  5%,  at  114. 

22.  An  investor  buys  100  shares  of  stock  at  110^,  holds 
the  stock  2  years,  receives  8  quarterly  dividends  of  1^^%, 
and  sells  it  at  113|.  Is  this  better  than  to  have  invested  his 
money  for  the  same  time  at  5%  ?    State  the  two  incomes. 

23.  A  man  buys  100  shares  of  stock  when  quoted  at  74|, 
holds  the  stock  two  years,  receives  8%  in  dividends,  and 
then  sells  it  at  72.  Compare  his  gain  or  loss  with  that 
resulting  from  investing  his  money  in  a  savings  bank  so 
that  it  earns  3%  compound  interest.  \  >^ 


BUYING  PRODUCE  219 

BUYING  PRODUCE 

224.  Large  dealings  in  produce.  A  man^s  work  may  lead 
him  into  large  dealings  in  the  products  of  the  soil.  These 
products  are  bought  and  sold  in  large  quantities  in  great 
auction  houses,  known  by  various  names,  such  as  the  Board 
of  Trade,  the  Produce  Exchange,  and  the  Cotton  Exchange. 

Teachers  should  not  require  these  business  customs  to  be  memo- 
rized but  should  seek  to  make  the  transactions  seem  real  and  legitimate. 

225.  Buying  grain.  As  a  rule,  not  less  than  1000  bu.  of 
grain  are  sold  at  a  time  on  the  Board  of  Trade  at  Chicago, 
the  great  center  for  such  transactions.  The  broker  charges 
J/  per  bushel  for  buying,  and  the  same  for  selling.  The 
quotations  are  by  the  number  of  cents  to  the  bushel  and 
always  vary  by  multiples  of  yi^/  per  bushel. 

226.  Buying  pork.  As  a  rule,  not  less  than  250  bbl.  of 
pork  are  sold  on  the  exchanges.  The  broker's  com- 
missions are  2j/  per  barrel  for  buying,  and  the  same  for 
selling.  The  quotations  are  by  the  number  of  dollars  to 
the  barrel  and  always  vary  by  multiples  of  2^f  per  barrel. 

In  all  of  the  following  examples  remember  the  broker's  com- 
missions as  stated  above. 

WRITTEN   EXERCISE 

1.  What  is  the  cost  of  3000  bu.  of  wheat  quoted  at  91  J/? 

2.  If  a  man  buys  5000  bu.  of  wheat  at  89y\/  and  sells 
it  at  91  J/,  how  much  does  he  gain? 

3.  If  a  dealer  buys  6000  bu.  of  corn  at  47^^/  and  sells 
'it  at  46 J/,  how  much  does  he  lose? 

4.  If  a  firm  of  produce  dealers  buys  750  bbl.  of  pork  at 
$12.72^,  and  sells  it  at  $13.20,  what  is  the  gain? 


220  BUYING  PRODUCE 

227.  Buying  lard.  This  is  one  of  the  leading  products  of 
the  central  part  of  our  country.  As  a  rule,  not  less  than 
250  tierces  are  sold  on  the  exchanges.  A  tierce  is  340  lb. 
The  broker  charges  2  J/  per  tierce.  The  quotations  are  in 
dollars  per  tierce. 

228.  Buying  cotton.  This  is  the  great  product  of  the 
South.  As  a  rule,  not  less  than  100  bales  are  sold  on  the 
exchanges.  A  bale  is  considered  as  500  lb.  The  broker 
charges  $5  per  100  bales.  The  quotations  are  in  cents 
per  pound,  and  vary  by  hundredths  of  a  cent. 

229.  Buying  coffee.  This  is  one  of  the  chief  imported 
products  dealt  in  on  the  exchanges.  As  a  rule,  not  less 
than  250  bags  are  sold.  A  bag  is  considered  as  130  lb. 
The  broker  charges  $10  per  250  bags.  The  quotations  are 
in  cents  per  pound. 

In  all  of  the  examples  remember  the  broker's  comm.issions. 

WRITTEN   EXERCISE 

1.  What  will  1250  bags  of  coffee  cost  at  8.42/? 

2.  What  will  750  tierces  of  lard  cost  at  $7.02  ? 

3.  What  will  3000  bales  of  cotton  cost  at  12.30/  ? 

4.  What  will  1000  tierces  of  lard  cost  at  $6.97^? 

5.  What  will  2500  bales  of  cotton  cost  at  11.75/? 

6.  If  a  man  buys  1500  tierces  of  lard  at  $6.87^,  and 
sells  it  at  $6.82^,  how  much  does  he  lose? 

7.  A  man  buys  250  bags  of  coffee  at  8.25/,  and  sells  it 
at  8.60/.    Does  he  gain  or  lose,  and  how  much  ? 

8.  A  cotton  factory  buys  500  bales  at  10.61/,  300  bales 
at  10.68/,  and  200  bales  at  10.75/.    What  is  the  cost? 

9.  A  dealer  buys  1200  bales  of  cotton  at  11.50/  and 
sells  it  at  11.61/.    Does  he  gain  or  lose,  and  how  much  ? 


INDUSTRIAL  PROBLEMS  221 

INDUSTRIAL    PROBLEMS 

230.  Problems  concerning  our  various  industries.  These 
problems  may  be  used  when  the  industries  are  being  studied 
in  geography.    In  general  they  involve  percentage. 

WRITTEN   EXERCISE 

1.  If  when  we  had  a  population  of  79,374,120  there  were 
661,451  persons  engaged  in  the  cloth  industry,  one  person 
out  of  how  many  was  engaged  in  this  work? 

2.  There  were  297,929  wage  earners  in  the  cotton  indus- 
tries of  our  country  in  a  certain  year,  and  they  received 
$84,909,765  a  year.  There  were  also  4713  salaried  clerks 
and  officials,  receiving  in  all  $7,121,343  a  year.  What  was 
the  average  income  of  each  class  per  capita? 

3.  If  our  factories  produce  $297,000,000  worth  of  woolen 
goods  in  a  certain  year,  and  the  materials  cost  61%,  the 
labor  19%,  the  salaries  of  officers  2%,  and  the  miscellaneous 
expenses  6%  of  this  sum,  how  much  is  expended  for  each 
of  these  items,  and  how  much  is  left  for  profit? 

4.  Of  all  the  timber  cut  in  this  country  in  a  certain  year, 
21^%  was  white  pine,  9.8%  was  hemlock,  4.2%  was  spruce, 
27.8%  was  yellow  pine,  and  12.8%  was  oak.  We  averaged 
2,530,000  M  ft.  that  year,  B.M.  How  many  feet  of  each  of 
these  woods  were  cut?    How  many  of  all  the  other  woods? 

5.  This  timber  was  worth,  on  an  average,  $2.18  per  M, 
standing,  and  $6.28  when  ready  for  the  mill.  How  much 
did  the  cutting  and  logging  add  to  the  value  of  the  total  ? 

6.  Out  of  this  increase,  $1.76  per  M  went  for  wages,  and 
94/  for  other  expenses,  the  rest  being  profit.  What  was 
the  total  profit? 


222  INDUSTRIAL  PROBLEMS 

7.  If  it  costs  $1.55  a  ton  to  manufacture  ice,  and  the 
wholesale  price  is  $2  a  ton,  what  is  the  per  cent  of  profit 
to  the  manufacturer? 

8.  The  value  of  our  leather  product  in  a  certain  year 
was  $204,000,000,  an  increase  of  18|f%  in  10  years. 
What  was  the  value  10  years  before? 

9.  The  value  of  the  shoes  manufactured  in  this  country 
in  a  certain  year  was  $262,700,000,  an  increase  of  18  J  %  in 
10  years.    What  was  it  10  years  before? 

10.  At  the  opening  of  the  century  the  amount  of  money 
invested  in  this  country  in  the  production  of  leather  was 
$174,000,000,  an  increase  of  77|J%  over  the  amount  10 
years  before.    What  was  the  amount  then? 

11.  In  a  certain  year  we  produced  67,890,000  pairs  of 
boots  and  shoes  for  men,  21,110,000  for  boys,  65,000,000 
for  women,  42,000,000  for  girls  and  children,  17,000,000 
pairs  of  slippers,  and  6,000,000  other  pairs.  The  men's 
boots  and  shoes  were  what  per  cent  of  the  total? 

12.  Some  of  the  leather  that  year  went  into  2,895,700 
dozen  pairs  of  gloves,  of  which  87%  were  for  men.  How 
many  gloves  were  produced  for  women  and  children? 

13.  In  a  certain  year  we  had  134,000  wage  earners  engaged 
in  making  cotton  cloth,  and  they  received  $46,900,000. 
Ten  years  before  that  we  had  89,000  wage  earners,  and 
they  received  $33,820,000.  Had  the  wages  increased  or 
decreased  per  capita,  and  how  much? 

14.  When  New  York  City  had  a  population  of  3^  mil- 
lions it  manufactured  411,000  tons  of  ice  a  year,  while 
New  Orleans,  with  a  population  of  300,000,  manufac- 
tured 140,000  tons.  The  population  and  ice  product  of 
New  Orleans  are  what  per  cents  of  those  of  New  York? 
Why  does  the  former  manufacture  relatively  more  ? 


GENERAL  PROBLEMS  223 

15.  In  a  year  when  our  flour  mills  produced  $589,950,- 

000  of  flour,  our  meat  products  were  worth  33  J  %  more. 
What  was  the  value  of  the  meat  products  ? 

16.  In  a  year  when  our  wool  products  amounted  to 
$446,740,000,  this  was  75%  more  than  the  value  of  our 
boot  and  shoe  products.    What  was  the  value  of  the  latter? 

17.  In  a  year  when  our  mines  produced  610,815,384  lb. 
of  copper,  the  total  output  was  worth  $73,297,846.08, 
which  was  20%  more  per  pound  than  it  was  worth  five 
years  before.    What  was  it  worth  per  pound  then? 

18.  In  a  year  when  the  wheat  crop  of  the  world  amounted 
to  3,124,422,000  bu.,  we  produced  22(^0  of  the  total,  and 
Canada  produced  15%  as  much  as  we  did.  How  many 
bushels  did  Canada  and  the  United  States  each  produce? 
How  many  together  ? 

19.  Suppose  the  grain  elevators  of  Duluth  to  have  a 
capacity  of  34  million  bushels.  Estimating  a  bushel  as 
\\  cu.  ft.,  what  is  this  capacity  in  cubic  feet?  (It  would 
be  interesting  to  see  how  many  times  the  volume  of  your 
schoolroom  this  is.) 

20.  Of  three  great  flour  mills  of  Minneapolis,  if  one  has 
a  capacity  of  28,000  bbl.  a  day,  a  second  of  3f  %  less,  and 
a  third  of  33  J  %  less  than  the  second,  and  all  should  run 
at  their  full  capacity  for  300  working  days  of  a  year,  how 
many  barrels  would  they  produce? 

21.  In  a  certain  state  it  takes  21  lb.  of  milk  to  make 

1  lb.  of  butter,  while  it  takes  22  lb.  in  a  second  state, 
23  lb.  in  a  third,  and  24  lb.  in  a  fourth.  The  first  state 
takes  what  per  cent  less  than  the  second  ?  The  second 
what  per  cent  more  than  the  first?  The  fourth  what  per 
cent  more  than  the  third?  The  third  what  per  cent  less 
than  the  fourth? 


/ 


224  INDUSTRIAL  PROBLEMS 

231.  Our  sugar  industry.  This  country  produces  about 
500,000  tons  of  sugar  a  year,  the  greater  part  being  made 
from  sugar  cane,  and  the  rest  from  beets.  At  present  the 
chief  beet-sugar  producing  states  are  California,  Michigan, 
Colorado,  and  Utah.    Our  cane  sugar  comes  from  Louisiana. 

WRITTEN   EXERCISE 

1.  If  2457  tons  of  beet  sugar  are  worth  $275,184,  what 
is  the  average  price  per  ton?  What  would  it  be  if  the 
price  were  decreased  2^%? 

2.  If  23,241  tons  of  sugar  beets  are  worth  $92,964,  what 
is  the  average  price  per  ton?  What  would  it  be  if  the 
price  were  increased  7J%  ? 

3.  If  we  manufacture  5325  tons  of  maple  sugar  in  a  year 
and  300,000  tons  of  cane  sugar,  the  amount  of  maple  sugar 
is  what  per  cent  of  that  of  cane  ? 

4.  In  a  year  when  we  had  132,441  acres  planted  to  sugar 
beets,  the  average  yield  was  6  tons  to  the  acre.  What  was 
the  value  of  the  crop  at  $4.10  a  ton? 

5.  When  we  produced  300,000  long  tons  of  cane  sugar  and 
195,000  long  tons  of  beet  sugar,  how  many  pounds  of  each 
did  we  produce?    Each  was  what  per  cent  of  the  sum? 

6.  If  the  world's  production  of  beet  and  cane  sugar  in 
one  year  is  9,835,392  tons,  and  the  cane  sugar  is  839,595 
tons  more  than  one  third  of  the  total,  how  much  beet  sugar 
is  produced? 

7.  If  we  have  1970  wage  earners  employed  in  making 
beet  sugar,  and  their  wages  are  $1,091,380,  and  if  we  pay 
100%  more  to  each  salaried  person  employed  in  this  indus- 
try than  to  the  wage  earner,  and  if  these  salaries  amount 
to  $356,776,  how  many  salaried  persons  are  employed? 


IRON  WORKING  225 

Problems  in  Iron  Working 
written  exercise 

1.  What  is  the  cost  of  12'  8"  of  iron  rod,  2^  lb.  to  the 
foot,  at  If/  a  pound? 

2.  What  is  the  weight  of  a  steel  girder  26'  6"  long, 
weighing  42j  lb.  to  the  foot? 

3.  The  wooden  pattern  from  which  an  iron  casting  is 
made  weighs  6i%  as  much  as  the  iron.  The  pattern 
weighs  45|  lb.     How  much  does  the  casting  weigh? 

4.  If  steel  rails  weighing  80  lb.  to  the  yard  are  used 
between  New  York  and  Chicago,  a  distance  of  980  mi., 
how  many  tons  will  be  required  for  a  double-track  road? 

5.  An  iron  tire  expands  1^^%  on  being  heated  for  shrink- 
ing on  a  wheel.  A  wooden  wheel  needs  a  tire  4'  8"  in  diam- 
eter. If  the  circumference  is  3i-  times  the  diameter,  how 
much  longer  will  the  tire  be  when  thus  heated  ? 

6.  In  a  certain  blast  furnace  the  casting  machine  turns 
out  20  pigs  per  minute,  averaging  in  weight  110  lb.  each. 
If  this  machine  runs  at  this  rate  for  308  days,  16  hours 
a  day,  how  many  long  tons  of  pig  iron  will  it  turn  out  ? 

7.  A  cellar  window  3'  x  2'  is  to  be  fitted  with  an  iron 
grating.  This  is  to  be  made  by  constructing  an  iron 
frame  and  then  putting  in  cross  pieces  of  iron  rods  3" 
between  centers,  the  top  and  bottom  ones  being  3"  from 
the  window  casing.  The  iron  frame  weighs  2i  lb.  per 
running  foot,  and  the  rods  weigh  13  oz.  per  running  foot. 
What  will  the  grating  cost  at  61/  a  pound,  not  allowing 
for  corners  nor  for  welding  the  joints?  Draw  to  scale  a 
plan  of  the  grating. 


226  INDUSTRIAL  PROBLEMS 

Railway  Problems 
written  exercise 

1.  If  ties  are  8"  wide,  and  are  placed  18"  apart,  how 
many  ties  are  there  to  a  mile? 

2.  We  use  90  million  new  ties  a  year,  averaging  8"  x  6" 
X  8'  6".    How  many  cubic  feet  of  timber  do  we  use? 

3.  The  modern  coal  car  has  a  capacity  of  100,000  lb. 
At  35  cu.  ft.  to  the  ton  (of  2000  lb.),  what  is  the  volume? 

4.  The  Pikes  Peak  railway  makes  an  ascent  of  7552  ft. 
in  a  length  of  8|  mi.  What  is  the  average  gradient  (ratio 
of  ascent  to  length)  ? 

5.  The  rails  are  usually  30'  long  and  often  weigh  80  lb. 
to  the  yard.  If  a  man  carries  160  lb.,  how  many  men  will 
it  take  to  carry  a  rail? 

6.  The  standard  gauge  in  America  and  England  is  4'  8 J". 
Express  this  in  meters,  as  used  in  most  European  countries, 
the  meter  being  39.37  in. 

7.  The  standard  American  gauge  (see  Ex.  6)  is  J  more 
than  the  gauge  of  a  certain  mountain  road.  What  is  the 
gauge  of  the  latter  ? 

8.  If  the  cost  of  maintaining  the  single  track  of  a  certain 
railway  averages  $846  a  mile,  what  is  the  cost  of  maintain- 
ing its  450  mi.  of  double  track  ? 

9.  In  a  year  when  our  country  had  1,189,000  men 
employed  in  the  railroad  business,  4%  were  employed  as 
engineers.  The  average  wages  for  engineers  that  year 
were  $3.84  a  day,  which  was  20%  more  than  the  average 
wages  for  conductors.  There  were  35,070  conductors  em- 
ployed that  year.  How  much  more  was  the  total  paid  for 
engineers'  wages  than  for  conductors'? 


OCEAN  TRAFFIC  227 

232.  The  great  ocean  steamers.  Some  idea  of  the  great 
shipping  industry  may  be  obtained  by  thinking  that  in  one 
year  857,000  immigrants  (steerage  or  third-cabin  passen- 
gers) came  to  our  country,  besides  the  first-  and  second- 
cabin  passengers.  A  large  ocean  steamer  has  a  capacity 
of  over  2,000,000  cu.  ft.,  perhaps  a  thousand  times  the 
capacity  of  your  recitation  room. 

WRITTEN  EXERCISE 

1.  One  of  the  fastest  day's  runs  recorded  for  a  steamer 
is  601  knots.    How  many  statute  miles  is  this  ? 

2.  A  certain  ocean  steamer  can  carry  3192  persons, 
including  the  crew.  The  crew  number  12%  as  many  as 
the  passengers.    How  many  are  there  of  each? 

3.  Prior  to  1860  the  best  steamship  record  between  New 
York  and  Queenstown  was  9  da.  2  hr.  When  it  was  reduced 
to  5  da.  7  hr.,  what  was  the  per  cent  of  reduction? 

4.  To  build  one  of  the  large  Atlantic  steamers,  1400 
plates  of  steel  were  used  in  the  hull  alone.  They  weighed 
4  long  tons  each.  How  many  tons  did  they  all  weigh? 
How  many  pounds? 

5.  A  steamer  carries  350  first-cabin  passengers,  48  %  as 
many  in  the  second  cabin,  and  400%  as  many  in  the  third 
cabin  (steerage)  as  in  the  other  two  together.  How  many 
passengers  does  it  carry? 

6.  A  20,000-ton  boat  carries  12  times  as  much  freight  as 
the  old-style  ocean  steamers,  makes  25%  better  time,  and 
the  expenses  are  only  4  times  as  much.  In  one  year  such 
a  modern  boat  will  do  how  many  times  the  work  of  the  old 
kind?  At  the  same  cost,  it  will  carry  how  many  times  as 
much  freight? 


228  INDUSTRIAL  PROBLEMS 

233.  Problems  in  meteorology.  Problems  concerning  rain- 
fall, temperature,  and  the  general  state  of  the  weather  are 
called  problems  in  meteorology.  They  are  so  related  to 
agriculture  as  to  have  a  place  among  industrial  problems. 

WRITTEN  EXERCISE 

--^  1.  What  is  the  weight  of  an  inch  of  rainfall  upon  an  acre, 
taking  the  weight  of  1  cu.  ft.  of  water  as  1000  oz.  ?  What 
is  it  on  a  200-acre  farm?    Answer  in  tons. 

2.  The  lowest  daily  temperatures  registered  during  a 
certain  week  in  January,  in  Buffalo,  were  7°,  3.6°,  —  9°  (9° 
below  zero),  6°,  —  3°,  0°,  8°.  What  is  the  average  of  these 
readings? 

3.  In  our  common  Fahrenheit  (F.)  thermometer  the  freez- 
ing point  of  water,  32°,  is  the  0°  in  the  Centigrade  (C.) 
thermometer,  and  the  boiling  point,  212°,  is  the  100°  in  the 
Centigrade.  Express  4°  C.  in  Fahrenheit,  and  62°  F.  in 
Centigrade.    Draw  each  thermometer  to  scale. 

4.  A  barometer  registered  29.024  in.  on  Monday.  In  the 
next  4  days  it  rose  0.135  in.,  0.044  in.,  0.095  in.,  and  0.573 
in.  On  Saturday  and  Sunday  it  fell  0.021  in.  and  0.417  in. 
What  was  the  Friday  reading?  the  Sunday  reading  ?  What 
were  the  weather  indications  on  Friday?  on  Sunday? 

A  rising  barometer  indicates  fair  weather.  When  the  mercury 
falls  rapidly  a  storm  is  indicated. 

6.  The  mean  (average)  annual  rainfall  at  Mobile  is  62.2 
in.  ;  at  Sacramento,  20.9  in. ;  at  Denver,  14.5  in. ;  at  Indian- 
apolis, 43  in. ;  at  Des  Moines,  33.1  in. ;  at  St.  Paul,  27.5  in. ; 
.  at  St.  Louis,  41.1  in. ;  and  at  Portland,  Oregon,  46.8  in. 
Taking  the  weight  of  1  cu.  ft.  of  water  as  62.5  lb.,  what  is 
the  weight  of  water  annually  falling  on  a  square  mile  in 
each  of  these  cities  ?    Answer  in  tons. 


METEOROLOGY  229 

6.  If  light  travels  186,000  mi.  per  second,  and  it  takes 
it  8.158J  sec.  to  come  from  the  sun  to  the  earth,  what  is 
the  distance  traveled? 

7.  Water  is  composed  of  two  gases,  oxygen  and  hydro- 
gen, 88.89%  by  weight  being  oxygen.  What  is  the  weight 
of  the  hydrogen  in  a  cubic  foot  of  water? 

8.  The  air  is  composed  of  two  gases,  oxygen  and  nitrogen . 
In  every  cubic  foot  of  air  there  are  345.6  cu.  in.  of  oxygen. 
What  per  cent  of  the  volume  of  the  air  is  nitrogen  ? 

9.  A  certain  cirrus  cloud  is  observed  to  be  6  mi.  above 
■  the  earth,  or  240%  higher  than  a  certain  rain  cloud  observed 

a  few  hours  before.    How  high  was  the  rain  cloud  ? 

10.  At  the  temperature  when  sound  travels  1120  ft.  per 
second,  what  is  the  distance  of  a  thunder  cloud  in  which 
lightning  is  seen  17f  sec.  before  the  thunder  is  heard? 

11.  If  a  large  drop  of  rain  falls  at  the  rate  of  20  ft. 
per  second,  and  a  small  one,  blown  by  the  wind,  only  2h^o 
as  fast,  how  long  will  it  take  the  small  one  to  reach  the 
earth  from  a  cloud  2\  mi.  high? 

12.  The  wind  pressure  in  a  hurricane  has  been  known  to 
be  as  great  as  49.2  lb.  per  square  foot.  In  such  a  storm 
how  many  tons  pressure  on  the  side  of  a  large  office 
building  104  ft.  long  and  308  ft.  high? 

13.  In  a  great  storm  the  velocity  of  the  wind  often 
reaches  88  ft.  per  second.  What  is  then  its  velocity  per 
minute?  In  a  hurricane  it  has  been  known  to  be  66f  % 
greater.    What  is  then  its  velocity  per  hour? 

14.  When  the  mercury  in  the  barometer  is  at  30  in.,  the 
pressure  of  air  on  every  square  inch  of  surface  is  15  lb. 
What  is  the  pressure  on  a  pane  of  glass  2  ft.  by  3  ft.,  when 
the  increased  air  pressure  forces  the  mercury  up  to  31  in.? 
Why  does  the  glass  not  break? 


230  POWERS  AND  ROOTS 


POWERS  AND  ROOTS 


234.  Square  numbers  and  square  roots.    If  a  square  has  a 
side  4  units,  it  has  an  area  16  square  units.     Therefore  16 
is  called  the  square  of  4,  and  4  the  square  root 
of  16. 


235.  Square   roots   of   areas.     Therefore,    con- 
sidering the  abstract  numbers  representing  the 
sides  and  area, 

The  side  of  a  square  is  the  square  root  of  its  area. 

236.  Writing  squares  and  roots.  The  square  of  4  is  written 
4^ ;  the  square  root  of  16  is  written  Vl^. 

237.  Perfect  squares.  A  number  like  16  is  2^  perfect  square, 
but  10  is  not  a  perfect  square.  We  speak,  however,  of 
VTo  =  3.16+,  because  3.16^  nearly  equals  10. 

238.  Square  roots  of  perfect  squares.    Square  roots      ^ 

of  perfect  squares  may  often  be  found  by  factoring.      ^ 

For  example,         V441  =  V3  x  3  x  7  x  7  7 

=  V21  X  21  =  21. 


ORAL    EXERCISE 

State  the  square  roots  of  the  numbers  in  Exs,  1—8  : 
1.  64,  2.  9.  3.  81.  4.  49. 

6.  121.  6.  144.  7.  1600.  8.  4900. 

What  are  the  sides  of  squares  whose  areas  are  as  follows  f 
9.  64  sq.  in.  10.  49  sq.  ft.  11.  1.44  sq.  in. 

12.  0.25  sq.  ft.  13.  y-i^  sq.  yd.  14.    j-i^  sq.  in. 

State  the  perimeters  of  squares  whose  areas  are : 
15.  1.21  sq.  ft.  16.  0.49  sq.  ft.  17.  169  sq.  in. 


SQUARES  AND  ROOTS  231 

WRITTEN   EXERCISE 

By  factoring^  find  the  square  roots  of  the  following  : 
y     1.  625.  2.  324.  3.  484.  4.  729. 

5.  576.  6.  2304.  7.  1296.  8.  1089. 

9.  65.61.  10.  12.25.  11.  40.96.  12.  14,641. 

Find  the  sides  of  squares  whose  areas  are  as  follows: 
13.  4.84  sq.  in.        14.  1.96  sq.  ft.         15.  2.25  sq.  ft. 
16.  4.41  sq.  in.        17.  4356  sq.  in.        18.  15,625  sq.  in. 
19.  5929  sq.  yd.      20.  10.89  sq.  yd.      21.  0.1225  sq.  ft. 

Find  the  perimeters  of  squares  whose  areas  are  as  follows : 
22.  6561  sq.  ft.       23.  12,100  sq.  in.     24.  11,025  sq.  ft. 
25.  19,600  sq.  ft.     26.  146.41  sq.  in.    27.  20,736  sq.  in. 
28.  16,384  sq.  in.    29.  16,900  sq.  ft.    30.  129,600  sq.  in. 

31.  From  the  corner  of  a  square  piece  of  land  containing 
576  sq.  rd.  a  small  square  lot  containing  64  sq.  rd.  is  cut 
out.  Draw  the  plan  of  the  lots  and  find  the  perimeter 
of  each. 

32.  A  square  lot  has  an  area  of  169  sq.  rd.  How  far  is 
it  around  the  lot  ?  How  far  is  it  around  a  lot  of  four  times 
this  area?  The  second  perimeter  is  how  many  times  the 
first  ?  Plot  each  lot  to  a  scale. 

33.  A  man  has  two  adjacent  building  lots  fronting  on 
the  street,  each  lot  being  square.  The  area  of  the  two 
together  is  89  sq.  rd.,  that  of  the  larger  being  64  sq.  rd. 
What  is  the  frontage  of  the  lots? 

34.  A  square  lot  has  an  area  of  289  sq.  rd.  How  far  is 
it  around  the  lot?  (Try  the  prime  numbers  between  10  and 
20.)  How  far  is  it  around  a  lot  of  nine  times  this  area? 
The  second  perimeter  is  how  many  times  the  first? 


232 


POWERS  AND  ROOTS 


239.  Cube  numbers  and  cube  roots.  If  a  cube  has  an 
edge  3  units,  it  has  a  volume  27 
cubic  units.  Therefore  27  is  called 
the  cube  of  3,  and  3  the  cube  root 
of  27. 

240.  Cube  roots  of  volumes.    There- 
fore, considering  the  abstract  num- 
bers representing  the  edges  and  volume. 

The  edge  of  a  cube  is  the  cube  root  of  its  volume. 

241.  Writing  cubes  and  roots.    The  cube  of  3  is  written  3^ ; 

3  / 

the  cube  root  of  27  is  written  V27. 

242.  Powers.  Squares  and^  ciibes  are  called  jpowers.  We 
also  have  higher  powers,  like  the  fourth,  fifth,  and  so  on. 
Raising  to  powers  is  sometimes  called  involution ;  extract- 
ing roots,  evolution. 

243.  Cube  roots  of  perfect  cubes.  Cube  roots  of  per-  2)216 
feet  cubes  may  often  be  found  by  factoring.  2)108 

2)54 

,         3)27 

:V(2x3)x(2x3)x(2x3)  3)9 

:  ^6  X  6  X  6  =  6.  3 


For  example,     V2I6  =V2x2x2x3x3x3 


1.    V^. 
5.    V^. 


ORAL    EXERCISE 

-^^^125.  3.   -v^. 


4.   VI 000. 


6.   Va027.       7.   VO.125.       8.   V0.064. 


1.   V1331. 


WRITTEN   EXERCISE 


2. 


-^729. 


3.   V512. 


4.   V1728. 


5.   V15625.        6.    V2744.        7.   V4096.         8.    V5832. 
9.  What  is  the  edge  of  a  cube  of  volume  10,648  cu.  in.  ? 


280 

49 

1600 
40 

280 
7 

SQUARES  233 

244.  Letters  used  to  represent  numbers.  If  we  have  two 
letters,  like  x  and  y^  the  product  of  their  values  is  indicated 
by  xy.  If  a;  ==  5  and  3/  =  7,  then  xy  =  6  x  1  =  ^^,2xy  =  70, 
aj2  =  2^,  and  y^  =  49. 

This  is  all  the  work  with  letters  necessary  for  the  understanding  of 
square  root.  If  not  already  known,  a  few  minutes  of  drill  upon 
similar  work  will  suffice. 

245.  Square  on  the  sum  of  two  lines.    If  we  have  two  lines, 
/  and  n,  and  construct  a  square  on  their 
sum,  we  see  by  this  figure  that  there  are 
two  squares  and  two  rectangles,  /^,  n^,  and 
fn,  fn.    Therefore 

The  square  of  the  sum  of  two  numbers 
equals  the  square  of  the  first j  plus  twice  the 
product  of  the  first  and  second,  plus  the  square  of  the  second. 

That  is,  {f-^-nf  =f'^  +  2/^  +  ri^. 

246.  Illustrative  problem.    What  is  the  square  of  47  ? 

472  =  (40  4-  7)2  =  402  +  2  X  40  X  7  +  72 

=  1600  +  560  +  49  =  2209. 

ORAL    EXERCISE 

Square  as  in  §  245 : 

1.    15.           2.    31.           3.  52.  4.   22.  5.    2b. 

6.    14.           7.    41.           8.  51.  9.    61.  10.    72. 

11.    a-\'b,          12.    m  +  7^.          13.  f -{- n,  14.    a -{- x, 

15.    x-\-y.          16.    t^u.            17.  2-\-y,  18.    4. -\- x. 

State  the  square  root  of: 

19.    c2  +  2ccZ  +  d\  20.   30^  +  2  X  30  X  7  -f  7^. 

21.    t''-^2tu-\-  u\  22     202  4-  2  X  20  X  6  -f  6^. 


234 


POWERS  AND  ITOOTS 


247.  How  to  find  a  square  root.    Find  V289. 

Because  289  is  not  so  readily  factored  as  the  numbers  we  have 
considered,  we  take  another  method  of  finding  the  square  root. 

Imagine  a  square  containing  289  square    D^ g 

units  (Fig  I). 

The  greatest  square  of  tens  in  289 
(Fig.  I)  is  100  (Fig.  II),  for  202  ^^^  400, 
and  this  is  greater  than  289. 

Taking  away  10^,  or  100,  as  marked 
off  in  Fig.  Ill,  we  have  left  189,  as  shown 
in  Fig.  IV.  We  may  now  lay  Fig.  IV 
lengthwise  as  in  Fig.  V. 

Now  we  know  that  Fig.  V  has  an  area 
of  189  square  units  and  a  length  a  little 
over  (10  +  10)  units  (because  of  the  little 
square).    Therefore  if  we     J? Q 


Fig.  I 


FiG.n 


P 
Fig.  in 


Q 


Q 


divide  189  by  10  +10,  or 

20,  we  shall  find  nearly  the 

width  PB,  or  the  side  SC 

of  the  little  square  SCTQ. 

Dividing,    189  -^  20  =  9 

(nearly).    But  this  would 

make  the  total  length  RP  (Fig.  V)  equal 

10  +  9  + 10  =  29,  and  the  area  would  be 

9  X  29  =  261,  which  is  greater  than  189. 

Therefore  9   is  too  large.    In  the  same 

way,  8  is  found  to  be  too  large,  for  it  makes  the 

area   224.    But   7   is   found   to   be   just   right,    for 

7  X  (10  +  7  +  10)  =  7  X  27  =  189. 

Therefore  V289  =17. 

Again  we  see  the  truth  of  §  245,  for  10^  +  2  x  10 
X  7  +  72  =  100  +  140  +  49  =  289.     That  is.   Fig.   II  +  Fig.  IV 
=  Fig.  I  or  Fig.  HI.  ^ 

The  check  (or  proof)  for 
square  root  is,  of  course,  the 
squaring  of  the  result.  R 

Here  17^  =  289.  Fig.V 


B 


Fig.  IV 


P 


SQUARE  ROOT  235 

248.  This  explanation  may  also  be  given  as  follows : 

If  we  let  /=  the/ound  part  of  the  root, 

and  n  =  the  next  figure  of  the  root, 

then  (/+n)2=/2  +  2>  +  n2.  (§245) 

Therefore  if  we  take  away/2  (Fig.  II),  we  shall  have  2fn  +  n^ 
(Fig.  IV,  where  each  oblong  is/x  n,  and  the  small  square  is  n^). 

If  we  divide  this  by  2/,  we  shall  find  nearly  n,  as  in  Fig.  V, 
where  we  divided  by  2  x  10  to  find  7. 

Since  the  entire  explanation  of  square  root  depends  on  this  fact, 
teachers  are  advised  to  see  that  this  is  clearly  understood,  both  from 
the  figure  and  from  the  formula,  before  proceeding. 

289  contains /2  +  2fn  +  n^  (Fig.  I) 

/2  ==  100  (Fig.  II) 

2f=  20       189        '<  2fn  +  n^  (Fig.  IV) 

2/+  n  =  27        189        =  "  '< 

The  greatest  square  of  tens  in  289  is  100,  for  20^  is  greater 
than  289. 

This  is/2,  and  therefore /=  10,  for  10  is  evidently  the  square 
root  of  100. 

189  contains  2fn  +  n^,  because /2  has  been  subtracted  from  a 
number  containing  f^  -{-  2fn  +  n^. 

Dividing  this  by  2/ we  approximate  w,  and  n  =  7.  I.e.,  189  -f- 
20  =  7  (nearly),  for  8  and  9  would  be  found  to  be  too  large,  as  on 
p.  234. 

But  2/+  w  multiplied  by  n  equals  2/w  +  n^  (Fig.  V),  thus  com- 
pleting the  square. 

Therefore  289  =P  +  2 fn  +  n^  =  10^  +  2  x  10  x  7  +  7^  =  172. 

249.  The  square  root  of  common  fractions.  It  is  easy  to  find 
the  square  root  of  common  fractions.  For  since  (f )^  =  I, 
therefore  f  =  V|.    That  is, 

To  extract  the  square  root  of  a  common  fraction  take  the 
square  root  of  each  term. 


236 


POWERS  AND  ROOTS 


WRITTEN  EXERCISE 


1.    V3249. 


5.   V1681. 


2.  V3721. 

3.  V3969. 

4.  V5041. 

6.  V2209. 

7.  V2809. 

8.  V3481. 

10.  V5329. 

11.  V5929. 

12.  V6241. 

9.   V4489. 

Find  the  sides  of  the  squares^  given  the  areas : 
13.  6724  sq.  ft.  14.  9409  sq.  ft.  15.  7225  sq.  in. 

16.  7569  sq.  ft.  17.  7921  sq.  rd.  18.  8281  sq.  in. 

19.  9025  sq.  ft.         20.  6889  sq.  yd.  21.  9801  sq.yd. 

Find  the  value  of  the  following : 


22.    ViJ|.  23.    V^.        24.    V|e|.        25.    Vifff. 

26.    Vfo¥5.        27.    V^.        28.    V/^Vt-        29.    V^. 

250.  Number  of  figures  in  the  square  root.  It  is  easy  to  tell 
in  advance  the  number  of  figures  in  the  square  root  of  a 
perfect  square.     For 

The  square  of  units  has  2  figures  or  1  figure,  since 

92  =  81,  12  =  1. 

The  square  of  a  number  of  2  integral  places  has  4  or  3  integral 
places,  since 

992  =  9801,  102  =  100. 

The  square  of  a  number  of  3  integral  places  has  6  or  5  integral 
places,  and  so  on,  since 

9992  =  998,001,  1002  =  10,000. 

251.  If  a  square  numher  he  separated  into  periods  of  two 
figures  each,  beginning  at  the  decimal  point,  the  numher  of 
periods  will  eqiial  the  numher  of  figures  in  the  root. 

Thus,  V43W21  has  3  integral  places  ; 

Vl  .23*21      "     1        ''        and  2  decimal  places. 


SQUARE  ROOT  237 


352.  Square  root  with  decimals.    Find  Vl51.29. 

The  greatest  square  of  lO's  in  151.29  is  100.     This  is/^,  and 
therefore /=  10. 

Then  51.29  contains  2 /n  +  w2.  (Why  ^^'^ 


IS  this  I*) 

Dividing  by  2/(20),  we  find  n  ==  2.  ^     ^  ^^         -|^ 

We  have  now  found  /  +  n  =  12,  the  "  '^ 

square  being  100  +  44  =  144.  '^       ^/•-94 '^ 

Since  12  has  been  found,  let  us  call  .   "         "    ^ 

...     .,.       .        ,,       /.                  ..-     '  2/+n  =  24.3           7.29 

this  /  (tor  /ound).     Of  course,  this  is     -^ 

not  the  same  as  the  first  number  found ;  it  is  larger,  because  we 

have  found  more. 

7.29  contains  2  fn  +  n^,  because  we  have  subtracted /^  =  144. 

Dividing  by  2/  (24),  we  find  n  =  0.3. 

2  /  +  n  multiplied  by  n  equals  2  fn  -{-  n^,  the  rest  of  the  square. 

253.  From  the  examples  solved  we  see  that  the  following 
are  the  steps  in  extracting  square  root : 

1.  Separate  into  periods  of  two  figures  each,  beginning  at 
the  decimal  point.     (See  §  251.) 

2.  Find  the  greatest  square  in  the  left-hand  period  and 
subtract  it,  bringing  down^  the  next  period. 

That  is,  find/2,  ^^^^  greatest  square  of  lO's,  lOO's,  or  lOOO's,  etc., 
and  subtract  it,  leaving  as  a  remainder  2/^  +  iiP-. 

3.  Divide  the  remainder  by  twice  the  part  already  found. 
That  is,  divide  2  fti  +  n^  by  2/to  find  approxiiAately  n. 

4.  Add  the  number  thus  found  to  this  divisor,  and  multiply 
by  the  same  number. 

That  is,  add  n  to  2/  and  multiply  by  n,  obtaining  2/n  +  n^. 

5.  Subtract   this  result,  bring  down  the  next  period,  and 
proceed  as  in  3  and  4- 

That  is,  having  now  subtracted  a  new/^,  proceed  as  before. 


238 


POWERS  AND  ROOTS 


/. 


3.  110.25. 

6.  0.2809. 

9.  63,001. 

12.  96,275,344. 


11. 


WRITTEN  EXERCISE 

Extract  the  square  roots  in  Exs,  1-17 : 
1.    12,321.  2.    54,756. 

A,   8046.09.  5.    19.4481. 

^7.    1176.49.  8.    82.2649. 

10.    21,224,449.  11.    49,112,064. 

In  Exs.  13-18  carry  the  root  to  two  decimal  places  only. 
13.    2.  14.    5.  15.    7.  16.    8.  17. 

18.   Find    the    side    of    a    square    containing    1    acre 
(160  sq.  rd.). 

254.  Hypotenuse.    In   a   right-angled    triangle   the    side 
opposite  the  right  angle  is  called  the  hypotenuse. 

255.  Square  on  the  hypotenuse.    If 

a  floor  is  made  up  of  triangular  tiles 
like  this,  it  is  easy  to  mark  out  a 
right-angled  triangle.  In  the  figure 
it  is  seen  that  the  square  on  the 
hypotenuse  contains  8  small  tri- 
angles, while  each  square  on  a  side 
contains  4  such  triangles.    Hence 

The  square  on  the  hypotenuse  equals  the  sum  of  the  squares 
on  the  other  two  sides. 

256.  This  is  true  for  any  right-angled  triangle.  We  see  that 
if  the  4  triangles,  1  +  2  +  3  +  4,  are  taken 
away  from  this  figure,  there  remains  the 
square  on  the  hypotenuse.  But  if  we  take 
away  the  2  shaded  rectangles,  which  equal 
the  4  triangles,  there  remain  the  squares 
on  the  two  sides.  Therefore  the  square  on 
the  hypotenuse  must  equal  the  sum  of  these  two  squares. 


W/'^^^//'^^^; 

Vs 

\       ^ 

SQUARE  ROOT  239 

257.  Illustrative  problem,    li  AB  =  12,  and  AC  =  9j  how 
long  is  J5C  ?  Q 

Since  AB^  +  AC^  =  BC% 

therefore  122  +  92  =  ^c^^ 

or  144  +  81  =  225  =  BC%  ~2 IT 

and  V226  =  BC.    Therefore  5C  =  15. 

WRITTEN  EXERCISE 

1.  How  long  is  the  diagonal  of  a  hall  51  ft.  by  68  ft.? 

2.  How  long  is  the  diagonal  of   a   square   containing 
4  sq.  ft.  ?    (Two  decimals.) 

3.  The  two  sides  of  a  right-angled  triangle  are  20  in.  and 
30  in.    Find  the  hypotenuse.    (Two  decimals.) 

4.  The  two  sides  of  a  right-angled  triangle  are  57  in.  and 
76  in.    Find  the  hypotenuse. 

5.  What  is  the  direct  distance  from  the  cornice  of  a 
100-ft.  building  to  a  spot  75  ft.  from  the  foot? 

6.  Find  the  length  of  the  hypotenuse  when  the  sides  are 
321  in.  and  428  in.  j  40  in.  and  75  in. ;  72  ft.  and  135  ft. 

/  7.  A  telegraph  pole  is  set  perpendicular  to  the  ground, 
and  a  wire  is  fastened  to  it  18  ft.  from  the  ground,  and 
then  to  a  stake  13  ft.  6  in.  from  the  foot  of  the  pole,  so 
as  to  hold  it  in  place.    How  long  is  the  wire  ? 

8.  A  derrick  for  hoisting  coal  has  its 
arm  27  ft.  6  in.  long.  It  swings  over 
an  opening  22  ft.  from  the  base  of  the 
arm.  How  far  is  the  top  above  the 
opening  ? 

Reversing  the  procedure  in  §  255,  the  square  on  either  side 
equals  the  difference  of  what  squares? 


240  POWERS  AND  ROOTS 

Find  to  two  decimal  places  the  hypotenuse  of  each  of  the 
right-angled  triangles  of  which  the  sides  are  here  given  : 

9.   35  ft.,  2Q  ft.  10.    81  ft.,  35  ft. 

11.    10  rd.,  13  rd.  12.   42^  ft.,  63i  ft. 

13.    4.5  in.,  7.2  in.  14.    6.25  in.,  7.5  in. 

It  is  a  good  exercise  to  make  up  problems  like  those  in  Exs.  15-19. 

15.  A  room  is  16  ft.  long,  12  ft.  wide,  and  9  ft.  high. 
How  far  is  it  from  an  upper  corner  diagonally  through  the 
room  to  the  opposite  lower  corner?    (Two  decimals.) 

First  draw  the  picture.  Then  find  the  hypotenuse  on  one  wall. 
Then  find  the  hypotenuse  required. 

16.  How  long  is  the  diagonal  of  a  cube  whose  volume 
is  8  cu.  in.?     (Two  decimals.) 

First  find  the  edge.     Then  proceed  as  in  Ex.  15. 

17.  A  school  flag  pole  is  broken  by  the  wind  16  ft.  from 
the  ground.  The  two  pieces  hold  together,  and  the  top  of 
the  pole  touches  the  ground  30  ft.  from  the  base.  Find  the 
length  of  the  pole. 

y    18.    If  I  start  to  row  directly  across  a  stream,  in  the  direc- 
tion AC,  at  the  rate  of  4  mi.  an  hour,  and  if  the  stream 

carries  me  in  the  direction  CB 
at  the  rate  of  3  mi.  an  hour,  my 
course  will  really  be  AB,  the 
result  of  these  two  motions. 
Suppose  I  row  at  the  rate  of 
4.5  mi.  per  hour,  and  the  stream 
flows  6  mi.,  what  is  my  rate  of  progress  ? 

19.  Suppose  I  walk  across  the  deck  of  a  steamer  at  the 
rate  of  4  mi.  per  hour,  while  the  boat  moves  at  the  rate  of 
8  mi.  per  hour,  at  what  rate  am  I  moving  ?  Answer  to  two 
decimal  places.    (Draw  a  plan  to  scale.) 


SQUARE  ROOT  241 

258.  Helpful  approximations.    Because  of  their   frequent 
use,  it  is  helpful  to  learn  the  following  approximations : 

V2  =  1.414       V3  =  1.732        V5  =  2.236      VlO  =  3.162 

259.  Illustrative   problem.     What   is   the   diagonal   of   a 
square  whose  side  is  7  in.  ? 

1.  The  square  on  the  diagonal  (hypotenuse)  is  49  sq.  in.  + 
49  sq.  in.  =  2  x  49  sq.  in. 

2.  Therefore  the  diagonal  =   v  2  x  49  in. 

3.  But  V2  X  49  =  V2  X  7 

4.  =  1.414  X  7  =  9.898. 

WRITTEN   EXERCISE 

1.  From  §  259  write  out  a  rule  for  finding  the  diagonal 
of  a  square  by  multiplying  its  side  by  a  certain  number. 

Find  the  diagonals  of  squares  with  sides  here  given : 

2.  19.2  in.        3.  32.8  in.         4.  683  ft.  5.  750  rd. 
6.    If  the  diamond  of  a  baseball  field  is  a  square  90  ft. 

on  a  side,  how  far  is  it  from  the  first  base  directly  across 
to  the  third? 

.    7.    A  gate  3  ft.  high  and  6  ft.  wide  is  to  be  braced  by  a 
stick  fastened  diagonally  across  it.    How  long  is  the  stick  ? 
Notice  that  Vis  =  V9  x  5  =  3  x  V5. 

8.  How  far  is  it  from  one  lower  corner  of  a  room 
directly  to  the  opposite  upper  corner,  the  dimensions  of 
the  floor  being  12'  x  16'  and  the  room  being  8  ft.  high? 

Find  the  diagonals  of  squares  with  areas  here  given : 
y  9.    81  sq.  ft.  10.    256  sq.  ft.  11.    6.25  sq.  ft. 

Find  the  sides  of  squares  with  diagonals  here  given  ': 
12.    14.14  in.  13.    4.242  in.  14.    7.07  ft.  /  2_ 


^ 


242 


POWERS  AND  ROOTS 


260.  How  to  find  a  cube  root.    Find  V2197. 

This  subject  may  be  omitted  without  interfering  with  the  work  that 
follows. 

Because  2197  is  not  so  readily  fac- 
tored as  the  numbers  we  have  consid- 
ered, we  take  another  method  of  finding 
the  cube  root. 

13 


2197 

1000 

300,  99,  399  1197 

1197 


Imagine  a  cube  containing  2197  cubic  units,  as  in  A,  where  of 
course  we  cannot  see  all  of  the  small  cubes. 

The  greatest  cube  of  tens  in  2197,  or  A,  is  1000  (B),  for  20^ 
=  8000,  and  this  is  greater  than  2197. 


/////// //A ' 
///////  /Am  I 


C  D 

Taking  away  10^,  or  1000,  as  marked  off  in  C,  we  have  left 
1197,  as  shown  in  D. 

We  may  now  lay  D  lengthwise,  as  in  E. 


CUBE  ROOT  243 

Now  we  know  that  the  solids  in  E  have  a  volume  of  1197 
cubic  units,  and  that  the  top  surface  of  the  three  larger  blocks 
has  an  area  of  3  x  10^  units,  or  300  square  units.  The  300 
represents  nearly  the  whole  top  area,  the  rest  being  that  of 
the  three  oblong  blocks  and  the  small  cube.  Therefore  if  we 
divide  1197  by  300  (sometimes  called  the  trial  divisor)^  we  shall 
have  approximately  the  thickness,  or  the  edge  of  the  small  cube. 
Dividing,  1197  -f-  300  =  3  (nearly). 

Now  if  3  is  the  thickness,  the  area  of  the  top  of  each  oblong 
piece  is  3  X  10,  and  the  area  of  the  three  is  3  x  3  x  10,  or  90. 
The  area  of  the  top  face  of  the  small  cube  is  3^,  or  9,  making  the 
area  of  the  top  of  these  four  pieces  90  +  9,  or  99.  Adding  the 
area  of  the  top  of  the  three  square  blocks,  we  have  300  +  99,  or 
399,  as  the  total  top  area. 

Multiplying  399,  the  number  of  square  units  in  the  top  area, 
by  3,  the  number  of  units  of  thickness,  we  have  1197,  the  num- 
ber of  cubic  units,  which  just  completes  the  cube,  D  applied  to 
B  just  making  C  or  A. 

261.  The  cube  oi  f  -\-n.  From  the  illustrations  in  §  260  we 
see  that  if  we  call  the  first  part  of  the  root  /  and  the  next 
part  n,  the  cube  oi  f  -\-  n  (A)  equals  the  cube  of  /  (B)  plus 
3  blocks,  each  with  a  volume  of  f^n,  plus  3  other  blocks 
(the  oblong  ones),  each  with  a  volume  of  fn^,  plus  the 
small  cube  with  a  volume  n^.    This  shows  that 

(/+  ny  =/^  +  Sf^n  +  Sfn^  +  n^. 

This  we  may  also  see  by  multiplying  (/+  n)^  by  /+  n,  or 
(10  +  3)2,  which  is  102  +  2  X  10  X  3  +  32^  ^y  10  +  3,  as  here 
shown. 

102  +  2  X  10  X  3   ^_  32 

10   +3 

102  X  3  +  2  X  10  X  32  +  33  multiplying  by  3 
108  +  2  X  102  X  3  +         10  X  32  "  "  10 

103  +  3  X  102  X  3  +  3  X  10  X  32  +  38  ^p  j^  3^2^  _^  3yy,2  _|.  ^3 


244  POWERS  AND  ROOTS 

WRITTEN  EXERCISE 

Find  the  cube  root  of  each  of  the  folloivhig  : 

1.    4913.  2.    6859.  3.    9261.  4.  5832. 

5.    13,824.  6.   19,683.  7.   29,791.  8.  4.^fim. 

9.    132,651.      10.    157,464.      11.   226,981.      12.  300,763. 

13.    551,368.      14.    753,571.      15.    884,736.      16.  941,192. 

17.   592,704.      18.    778,688.      19.   857,375.      20.  970,299. 

By  the  method  of  §  261,  find  the  cube  of  each  of  the 
following^  proving  the  result  by  multiplication : 

21.  12,  that  is,  10  +  2. 

(10  +  2)3  =  103  +  3  X  102  X  2  +  3  X  10  X  22  +  28 
=  1000  +  600  +  120  +  8  rz:  1728. 

22.  14.       23.  21.       24.  25.       25.  30. 

26.  ^n.  27.  60.      28.  75.      29.  99. 

262.  Number  of  figures  in  the  cube  root.  It  is  easy  to  tell 
in  advance  the  number  of  figures  in  the  cube  root  of  a 
perfect  cube.    For 

The  cube  of  units  has  3,  2,  or  1  figure,  since 

93  =  729,  43  =  64,  13  =  1. 
The  cube  of  a  number  of  2  integral  places  has  6,  5.  or  4  integral 
places,  since 

993  =  970,299,  40^  =  64,000,  10-^  =  1000. 
The  cube  of  a  number  of  3  integral  places  has  9,  8,  or  7  integral 
places,  and  so  on.    Therefore 

263.  If  a  cube  number  be  separated  into  periods  of  three 
figures  each,  beginning  at  the  decimal  point,  the  number  of 
periods  will  equal  the  number  of  figures  in  the  root. 


Thus,  Vl,771,561  has  3  integral  places ; 

V'26.463,592    "    1       "         and  2  decimal  places. 


CUBE  ROOT  245 


264.  Cube  root  by  the  formula  for  (/+n)^    1.  Find  V2 197. 

If  we  let  /=  the/ound  part  of  the  root, 

and  n  =  the  next  figure  of  the  root, 

then  (/+  n)3  =/3  +  3pn  +  3>2  +  n^.  (§  261) 

Therefore  if  we  take  away  /^  (B  on  page  242),  we  shall  have 
o/^n  -f  3/?i2  +  n^  (D,  page  242,  where  each  square  block  is  /^n, 
each  oblong  fn^,  and  the  small  cube  is  n^). 

If  we  divide  this  by  3/^,  we  shall  find  approximately  n  (as 
in  E,  page  242,  where  we  divided  the  number  of  units  of  volume 
by  the  number  of  units  of  area  of  the  three  squares). 

1 3  ^ 

2,197  -^2,197=  13 

3/2  3>  +  n2  3/2  +  3/n  +  n2    /^  =  1000 

300         99  399  1197  contains  3/2n  +  3>2  +  n3 

1197        =  ''  "         '< 

The  greatest  cube  of  tens  in  2197  is  1000,  for  20^  z=  8000,  and 
this  is  greater  than  2197.  Therefore /^  is  1000.  Since /^  =  1000, 
/is  10. 

The  remainder,  1197,  contains  3/2n  +  3/i2  +  n^^  because  from 
a  number  containing  (/+  n)^,  or  /^  +  3/2^  +  3/n2  +  n%  f^  has 
been  subtracted. 

Dividing  this  by  3/2  (as  seen  also  on  page  242),  we  approximate 
n,  and  w  =  3. 

Now  the  quantity  which  multiplied  by  n  equals  3/2n  +  3/n2  +  n^, 
and  thus,  with  the/3  already  found,  completes  the  cube  of/+n, 
is  3/2  +  3>  +  n2.     (See  also  page  242.) 

Therefore  we  add  to  3/^  the  quantity ,  that  will  make  this, 
that  is,  3/n  +  7i^,  Now  3>  +  n2  =  3  x  10  x  3  +  32  =  99,  and 
300  +  99  =  399. 

Multiplying  399  by  3,  the  result  is  1197,  exactly  completing 
the  cube. 

It  is  easily  seen  that  2197  must  be  the  cube  of  13,  for  (§  261) 
133  =  103  +  3  X  102  X  3  +  3  X  10  X  32  +  33  =  1000  +  900  +  270  +  9 
=  1000  +  1179,  which  are  exactly  the  numbers  above  subtracted 
from  2197,  leaving  no  remainder. 


246  POWERS  AND  ROOTS 


2.  Find  Vl,771,561. 

12     1           ^ 

1,771,561          Vl, 771 ,561 =121. 

Sn     3fn  +  n^    3/*«  +  3/w  +  w2      /s  =  i  000  000 

30,000      6400                36,400                          771  561  contains  3f^n  +  3//i2  +  n^ 

/=100 

728  000          =            "           "         " 

?i=    20 

43,200       361                 43,561                           43  561  contains      "           "         *' 

/=120 

43  561 

n=     1 

There  cannot  be  any  thousands  in  the  root,  for  1000^  =  1,000,- 
000,000,  and  this  is  larger  than  the  given  cube. 

The  greatest  cube  of  hundreds  in  .1,771,561  is  1,000,000,  because 
200^  is  larger  tfetn  the  given  number.      Therefore  /  =  100. 

Then  the  remainder,  771,561,  contains  Sf'^n  -f  3/^^  +  n% 
because /3,  or  1,000,000,  has  been  subtracted  from  a  number  con- 
taining/^  +  3/2n  +  3>2  +  n3. 

Because  this  contains  approximately  2f^n,  if  we  divide  by  3/^ 
(or  30,000)  we  shall  find  approximately  n.  We  therefore  find 
that  w  =  20. 

Adding  3>  +  n^,  or  3  x  100  x  20  +  202,  to 
3/2,  we  have  36,400  (as  explained  on  page  245). 
This  multiplied  by  20  (that  is,  by  n)  equals 
728,000,  thus  completing  the  cube  of  120. 

That  1,000,000  and  728,000  are  together 
the  cube  of  120  is  evident  from  the  fact  that 
1203  =  1003  +  3  X  1002  X  20  +  3  X  100  X  202 
+  203  (§  261)  =  1,000,000  +  600,000  -I- 120,000 
-f  8000  =  1,000,000  +  728,000. 

We  may  now  consider  120  as  the  found 
part  of  the  root,  and  proceed  as  before,  finding  n  =  1.    The  root 
is  therefore  121. 

The  annexed  arrangement  shows  all  of  the  necessary  figures, 
and  is  the  one  recommended  after  the  process  is  understood.  It 
simply  preserves  the  figures  actually  used  from  step  to  step,  not 
writing  the  others. 

In  case  there  are  more  figures  in  the  root  we  may  subtract  and 
proceed  as  before,  dividing  again  by  three  times  the  cube  of  the 
found  part. 


1      2      1 

1,771,561 
1 

300 

64 

364 

771 

728 

43200 

361 

43561 

43561 
43561 

CUBE  ROOT  247 

265.  The  following  are  therefore  seen  to  be  the  steps  in 
extracting  cube  root  : 

1.  The  number  being  already  separated  into  three-figure 
periods,  beginning  at  the  decimal  point,  find  the  greatest 
cube  in  the  left-hand  period.  This  is  the  cube  of  the  number 
represented  by  the  first  figure. 

2.  Subtract  this  cube,  bringing  down  but  one  period. 

3.  Divide  this  remainder  by  three  times  the  square  of  the 
found  part  considered  as  tens  (the  so-called  trial  divisor)  to 
find  the  next  figure. 

4.  To  three  times  the  product  of  the  tivo  parts  add  the 
square  of  the  second,  considered  as  units,  and  add  all  this 
to  the  trial  divisor,  thus  making  the  coinplete  divisor. 

5.  Multiply  the  complete  divisor  by  the  second,  thus  com- 
pleting the  cube  of  the  first  two. 

6.  Sicbtract  this,  bring  down  the  next  period,  and  proceed 
as  before. 

The  subject  of  cube  root  being  now  so  commonly  postponed  until 
algebra  is  studied,  a  more  extended  explanation  is  not  felt  to  be 
necessary. 

WRITTEN   EXERCISE 

Extract  the  cube  root  of  each  of  the  following : 

1.  2197.  2.  3375.  3.  2744. 

4.  68,921.  5.  74,088.  6.  91,125. 

7.  97,336.  8.  110,592.  9.  140,608. 

10.  205,379.  11.  250,047.  12.  4,330,747. 

13.  1,295,029.  14.  1,771,561.  15.  2,628,072. 

16.  4,096,000.  17.  4,826,809.  18.  50,653,000. 

19,  54,010,152.  20.  97,336,000.  21.  99,252.847. 

22.  91,733.851.  23.  0.114791256.  24.  34,645,976. 


248  MENSURATION 

MENSURATION 

266.  Ratio  of  circumference  to  diameter.  By  measuring 
several  circles,  dividing  each  circumference  by  its  diameter, 
and  taking  the  average  of  the  results,  the  circumference 
will  be  found  to  be  about  3}  times  the  diameter. 

267.  Value  of  tt.  It  is  proved  in  Geometry  that  this  ratio 
of  circumference  to  diameter  is  more  nearly  3.1416.  The 
ratio  is  denoted  in  mathematics  by  the  Greek  letter  tt  (pi). 

268.  Formula  for  circumference.  Therefore,  if  c  =  circum- 
ference, d  =  diameter,  and  r  =  radius,  we  have 

c 

whence  c  =  ird, 

or,  because  c?  =  2r,  c=irx2r  =  2'jTr 

=  2  X  3|  X  radius  (nearly). 

269.  Illustrative  problems.  1.  Required  the  circumference 
when  the  radius  is  7  in. 

c  =  2  7rr  =  2  X  3^  X  7  in.  =  44  in. 
More  exactly,  2  x  3.1416  x  7  in.  =  43.9824  in. 

2.  Required  the   diameter  when   the    circumference   is 

2827.44  in. 

c  2827.44  in.     ^^^  . 

Since  7rd  =  c,  d  =  — ,  or  d  =  -—r^rrz-z —  =  900  m. 

TT  3.1416 

ORAL   EXERCISE 

Using  tt  =  3^  =  ^y^-,  state  the  circumferences  of  circles  of 
diameters  as  follows : 

1.  7  in.     2.  21  in.    3.  14  in.      4.  70  in. 

5.  28  in.    6.  35  in.    7.  42  in.      8.  700  in. 

9.  77  in.    10.  140  in.   11.  280  in.    12.  350  in. 
13.  0.7  in.   14.  0.21  in.  15.  0.14  in.    16.  0.28  in. 


THE  CIRCLE  249 

WRITTEN   EXERCISE 

Find  the  circumference  (tt  =  3^),  given  the  diameter : 
^1.    68.2  in.  2.    48.3  ft.  3.   423  in. 

4.    5.11  ft.  5.   53.9  ft.  6.   6.37  in. 

7.    4.69  ft.  8.    58.1  in.  9.    6.02  ft. 

10.    13  ft.  6  in.         11.    17  ft.  8  in.  12.    64.4  ft. 

Find  the  diameter  (tt  =  3^),  given  the  circumference : 
13.   132  ft.  14.    5S^  ft.  15.   97f  ft. 

16.    176  in.  17.    770  ft.  18.    96|  ft. 

19.    68.2  in.  20.    3.96  ft.  21.    0.484  ft. 

Find  the  circumference  (7r==  3.1416),  given  the  diameter: 
22.    17  in.  23.    13  in.  24.    2.8  in. 

25.    4.37  in.  26.    2.25  ft.  27.    6  ft.  2  in. 

Find  the  diameter  (tt  =  3.1416),  given  the  circumference : 
28.    53.4072  in.        29.    84.8232  in.  30.    97.3896  in. 

31.    94.2478  ft.         32.    1^2.222^  ft.         33.    138.2304  ft. 

Find  the  circumference  (tt  =  3^),  given  the  radius: 
34.    49  in.  35.    77  in.  36.    91  in. 

37.    105  in.  38.    15.4  in.  39.    If  in. 

40.  What  is  the  diameter  of  a  water  tank  whose  circum- 
ference is  74.8  ft.  ?    (tt  =  3|.) 

41.  What  is  the  circumference  of  a  rod  whose  diameter 
as  measured  by  the  calipers  is  2.1  in.  ?    (tt  =  3|.) 

42.  What  is  the  circumference  of  a  wire  whose  diameter 
as  measured  by  the  calipers  is  0.63  in.  ?    (tt  =  3^.) 

43.  What  radius  must  be  used  in  drawing  a  pattern  for 
a  wheel  that  shall  be  91|  in.  in  circumference?    (tt  =  3|.) 


250  MENSURATION 

270.  Area  of  a  circle.  A  circle  can  be  separated  into  fig- 
ures which  are  nearly  triangles.  The  height  is  the  radius, 
and  the  sum  of  the  bases  is  the  circumference.    If  these 


were  exact  triangles  the  area  would  be  ^  x  r  x  c,  or  ^  re. 
It  is  proved  in  Geometry  that  this  is  the  true  area. 

271.  Given  the  radius,  to  find  the  area.    \i  a  =  area,  c  —  cir- 
cumference, and  r  =  radius, 

a  =  ^rc,  or,  because  c  is  the  same  as  2  vrr,  we  may  write 

r  X  t'Jrr 
a  =  ^7'  X  2  irr,  ov  a  = =  ttt*  . 


272.  The  area  of  a  circle  is  ir  times  the  square  on  the 
radius. 

273.  Illustrative  problem.    Eequired  the  area  of  a  circle 
whose  radius  is  5  in. 

a  =  7rr2  =  TT  X  25  sq.  in.  =  3.1416  X  25  sq.  in.  =  78.54  sq.  in: 

In  the  rest  of  the  problems  involving  tt,  use  the  value  3^  unless 
otherwise  directed. 

ORAL    EXERCISE 

State  the  area,  given  the  radius  as  follows: 

1.    7  in.  2.    70  in.  3.  ^\  in.  4.    J^  in. 

.    5.    If  you  take  a  radius  half  as  long,  the  area  will  be 

what  part  as  great? 

6.    If  you  double  the  length  of  the  radius,  the  area  will 

be  how  many  times  as  large? 


THE  CIRCLE  251 

274.  Illustrative  problem.  Eequired  the  radius,  the  area 
being  50.2656  sq.  in. 

a 

1.  Since  a  =  Trr^,  r^  =  - »  by  dividing  these  equals  by  ir. 

2.  50.2656  sq.  in.  -4-  3.1416  =  16  sq.  in. 

3.  Since  VT6^  =  4,  the  radius  is  4  in. 

WRITTEN   EXERCISE 

1.  What  is  the  area  of  the  cross  section  of  a  water  pipe 
that  is  2  in.  in  diameter? 

2.  How  many  square  feet  in  the  base  of  a  water  tank 
that  is  42  ft.  in  diameter  ? 

y     3.    A  horse  tethered  by  a  rope  21  ft.  long  can  graze  over 
how  many  square  feet  of  ground  ? 

4.  A  horse  tethered  by  a  rope  can  graze  over  3850  sq.  ft. 
of  ground.    How  long  is  the  rope? 

5.  How  long  is  the  equator  on  a  globe  12.67  in.  in  diam- 
eter? What  is  the  area  of  the  equator  circle  cut  from 
such  a  globe? 

6.  A  school  flag  pole  has  a  circumference  of  24.2  in.  at 
the  base.  What  is  the  diameter?  the  radius?  the  area  of 
a  cross  section? 

7.  What  is  the  area  of  the  cross  section  of  a  circular  iron 
beam  whose  circumference  is  31.416  in.?  (Use  7r  =  3.1416.) 
Suppose  the  circumference  were  53.4072  in.? 

8.  A  boy  has  a  ball  tied  to  a  string  1  yd.  6  in.  long.  As 
he  swings  it  around,  how  long  is  the  circumference  traveled 
by  the  ball  ?    What  is  the  area  of  the  circle  inclosed  ? 

9.  A  tinsmith  wishes  to  make  a  pattern  for  the  bottom 
of  a  pail,  the  area  being  154  sq.  in.,  and  to  allow  ^  in.  all 
around  for  soldering.  What  radius  should  he  use  in  draw- 
ing the  circle  ? 


252 


MENSURATION 


ORAL   EXERCISE 

1.    A  represents  a  cube  1  in.  on  an  edge.    What  is  its 
volume?    Suppose  it  were  2  in.  on  an  edge  ? 

2.    B  represents  half  of  a  cube  that  was 
1  in.  on  an  edge.     What   is  its  volume? 
Suppose  the   original  cube 
^  were  3  in.  on  an  edge?       |||| 

3.  What  is  the  volume  of  a  prism  1  in.  high, 
with  a  base  J  sq.  in.  ?    1  sq.  in.  ?    3  sq.  in.  ?  b 

4.  Suppose  the  area  of  the  base  in  C  is  5  sq.  in.,  what 
is  the  volume  of  the  lower  shaded  part 
that  is  1  in.  high  ?  What  is  the  total 
volume  ? 

275.  Volume  of  a  prism.  We  see  that, 
if  h  is  the  area  of  the  base  of  a  prism, 
h  is  the  height,  and  v  is  the  volume, 
V  =  bh. 

Pupils  should  be  led  to  read  their  own 
rules  from  all  such  formulas.     Thus, 

276.    The  volume  of  a  prism  equals  the  area  of  the  base 
multiplied  by  the  height. 

This  is  to  be  understood  with  the  meaning  given  in  §  38. 

State  the  volumes  of  prisms  with  bases  and  altitudes  as 
follows : 


5.  9  sq.  in.,  4  in. 

7.  16  sq.  in.,  5  in. 

9.  480  sq.  in.,  12^  in. 

11.  330  sq.  in.,  33^  in. 

13.  8000  sq.  in.,  75  in. 


6.    17  sq.  in.,  7  in. 
8.   440  sq.  in.,  25  in. 
in.,  50  in. 


10.    900  sq. 

14.    500  sq.  ft.,  lOj  ft. 


12.    480  sq.  in.,  16§  in. 


THE  PRISM  253 

WRITTEN    EXERCISE 

Find  the  volumes  of  prisms  with  bases  and  altitudes  as 
follows : 

1.    375  sq.  in.,  29  in.  2.    1.28  sq.  ft.,  3.2  in. 

3.    67.9  sq.  in.,  4.8  in.  4.    42.6  sq.  in.,  7.3  in. 

5.    61.3  sq.  ft.,  2.91  ft.  6.    62.8  sq.  in.,  3.17  in. 

Find  the  altitudes  of  prisms  with  volumes  and  bases  as 
follows: 

7.    243  cu.  in.,  29  sq.  in.  8.    783  cu.  in.,  87  sq.  in. 

9.    140  cu  in.,  17J  sq.  in.       10.    178i  cu.  in.,  19J  sq.  in. 

Find  the  volumes  of  rectangular  solids  as  follows: 

11.  42  in.  by  &.%  in.  by  3.5  in. 

12.  2.9  in.  by  3.8  in.  by  6.4  in. 

13.  3.91  ft.  by  4.27  ft.  by  6.8  ft. 

14.  2.8  ft.  by  3.25  ft.  by  4.75  ft. 

15.  6.5  ft.  by  4.75  ft.  by  3.25  ft. 

16.  21.3  in.  by  29.2  in.  by  3.7  in. 

yr  17.    The  area  of  one  face  of  a  cube  is  3721  sq.  in.    What 
is  the  volume  of  the  cube? 

/  ^  18.   A  prism  with  a  square  base  of  127.69  sq.  in.  is  twice 
as  high  as  it  is  wide.    Find  its  volume. 

19.  A  prism  has  a  square  base,  a  volume  of  4851  cu.  in., 
and  a  height  of  11  in.    Eequired  the  lengths  of  the  edges. 

20.  A  prism  has  a  square  base,  a  volume  of  1687^  cu.  in., 
and  an  altitude  that  is  half  its  width.    Find  its  altitude. 

If  the  altitude  equaled  the  width,  16 87 J  would  be  the  cube  of 
the  edge.  As  it  is,  1687 J  is  therefore  half  the  cube  of  the  side 
of  the  base. 


254  MENSURATION 

277.  Volume  of  a  cylinder.    The  same  reasoning  as  that 
employed  on  page  252  evidently  gives  the  volume  of  a 
^_— _— ^       cylinder.    Hence  we  may  say  that 

II  '^  ~  ^^* 

ml  278.   The  volume  of  a  cylinder  equals  the  area 

of  the  base  multiplied  by  the  height, 

279.  If  the  cylinder  is  the  common  one  with  a  circular 
base,  the  area  of  the  circle  is  irr'^  (§  271).  Therefore,  with 
such  a  cylinder,  „_ 

ORAL   EXERCISE 

State  the  volumes,  given  bases  and  altitudes  as  follows : 
1.    0.48  sq.  in:,  I  in.  2.    1.2  sq.  ft.,  j\  ft. 

3.    300  sq.  in.,  33j  in.  4.    150  sq.  in.,  50  in. 

5.    600  sq.  in.,  66§  in.  6.   80  sq.  in.,  12^^  in. 

WRITTEN   EXERCISE 

1.  Find  the  volume  of  a  water  tank  40  ft.  high  and  40  ft. 
in  diameter. 

2.  How  many  cubic  feet  in  a  log  16  ft.  long,  the  average 
diameter  being  1  ft.  11  in.? 

3.  How  many  gallons  (231  cu.  in.)  in  a  cylindrical  tank 
32  ft.  high  and  30  ft.  in  diameter? 

4.  Find  the  number  of  cubic  feet  in  a  boiler  15  ft.  long 
and  3  ft.  6  in.  in  diameter,  internal  measure. 

5.  Find  the  number  of  cubic  inches  in  a  pipe  18  ft.  long, 
4  in.  in  external  diameter,  the  metal  being  i  in.  thick. 

6.  What  is  the  volume  of  a  cylinder  with  radius  7  in. 
and  height  17  in.?  with  radius  9  in.  and  height  45  in.? 


CYLINDER  255 


ORAL   EXERCISE 


1.  If  we  slit  the  curved  surface  of  the  cylinder  shown 
on  page  254,  and  spread  it  out  flat,  what  will  it  become? 
How  may  we  find  the  area  of  this  surface  ?    Try  it. 

2.  What  is  the  area  of  the  curved  surface  of  a  cylinder 
6  in.  high  and  8  in.  around?     9  in.  high  and  9  in.  around? 

3.  How  many  square  feet  of  tin  are  needed  for  a  pipe 
8  ft.  long  and  6  in.  around,  allowing  1  sq.  ft.  for  overlapping? 

280.  Curved  surface  of  a  cylinder.  We  see  that  the  area  of 
the  curved  surface  of  a  cylinder  equals  the  product  of  the 
height  and  the  circumference. 

That  is,  if  c  =  circumference,  h  —  height,  and  a  =  area, 

a=  ch. 

Or,  if  r  =  radius  of  the  base,  i 

a  =  27rr  X  h. 

State  the  area  of  the  curved  surfaces  of  cylinders  with 
heights  and  circumferences  as  follows: 

4.    25  in.,  80  in.  -  5.    33^  in.,  69  in. 

6.    75  in.,  40  in.  7.    50  in.,  106  in.  i 

8.    66fin.,  48in.  9.    12^  in.,  24  in. 

10.    16§  in.,  36  in.  11.    33j  in.,  33  in. 

12.  How  many  square  inches  in  the  curved  surface  of  a 
wire  1  in.  around  and  200  ft.  long? 

13.  A  tin  cup  is  7  in.  around  and  3  in.  high,  both  meas- 
ures including  allowance  for  soldering.  How  many  square 
inches  of  tin  are  needed  for  the  curved  surface  ? 

14.  A  tin  water  pipe  has  a  circumference  of  9  in.  and 
a  length  of  10  ft.,  both  measures  including  allowance  for 
soldering.    How  many  square  inches  of  tin  are  needed  ? 


256  MENSURATION 


WRITTEN   EXERCISE 


1.  How  many  square  inches  of  surface  on  a  wire  10  ft. 
long  and  |  in.  in  circumference? 

2.  If  the  height  and  diameter  of  a  solid  cylinder  are 
both  7  in.,  what  is  the  total  area  of  surface? 

To  the  cylindrical  surface  add  the  areas  of  the  circles  forming 
the  top  and  bottom. 

3.  How  many  square  inches  of  tin  are  needed  for  a 
cylindrical  cup  4  in.  high  and  4  in.  in  diameter? 

4.  How  many  square  feet  in  the  curved  surface  of  a 
water  tank  that  is  40  ft.  high  and  127.3  ft.  around? 

5.  Write  a  rule  for  finding  the  circumference  of  a  circle, 
given  the  radius  ;  also  for  finding  the  area  of  a  circle. 

6.  How  many  square  feet  of  surface  on  the  outside  of 
a  smokestack  30  ft.  high  and  2  ft.  in  exterior  diameter? 

7.  The  curved  surface  of  a  granite  cylindrical  shaft, 
3  ft.  6  in.  in  diameter  and  22  ft.  3  in.  long,  is  to  be  polished. 
How  many  square  feet  of  surface  are  to  be  polished? 

8.  In  a  certain  factory  there  is  a  room  heated  by  210  ft. 
of  steam  pipe,  2  in.  in  diameter.  Eequired  the  radiating 
surface.  (That  is,  the  area  of  the  curved  surface  which 
radiates  the  heat.) 

9.  A  large  suspension  bridge  has  4  cables,  each  1872  ft. 
long  and  1  ft.  2  in.  in  diameter.  In  letting  the  contract 
for  painting  these  cables  it  is  necessary  to  know  their 
surface.    Compute  it. 

10.  In  making  metal  bedsteads  some  iron  rods  0.75  in. 
in  diameter  are  covered  with  thin  rolled  brass.  Suppose  a 
shop  needs  6000  ft.  of  such  rods,  how  many  square  feet  of 
rolled  brass  will  be  needed,  not  allowing  for  waste? 


PYRAMID 


257 


281o  Volume  of  a  pyramid.  If  we  construct  a  hollow 
prism  and  a  hollow  pyramid  of  the  same  base  and  height, 
filling  the  former  with  sand,  the  latter 
can  be  filled  three  times  with  the  same 
amount.     Therefore 

282.   The  volume  of  a  pyramid  equals 
one  third  the  product  of  its  base  and  height,    ^\  / 


ORAL  EXERCISE 


State  the  volumes  of  pyramids  with  bases  and  altitudes 
as  follows: 


1. 

75  sq.  ft.,  7  ft. 

2. 

21  sq.  ft.,  9  ft. 

3. 

33  sq.  ft.,  6  ft. 

4. 

120  sq.  ft.,  7  ft. 

5. 

70  sq.  in.,  9  in. 

6. 

63  sq.  ft.,  12  ft. 

7. 

39  sq.  in.,  10  in. 

8. 

38  sq.  in.,  15  in. 

9. 

450  sq.  in.,  20  in. 

10. 

480  sq.  in.,  10  in 

WRITTEN   EXERCISE 

Find  the  volumes  of  pyramids  with  bases  and  altitudes 
as  follows : 

y  1.    129.3  sq.  in.,  3.72  in.  2.    702.39  sq.  in.,  16.8  in. 

^  3.    202.11  sq.  ft.,  8.92  ft.  4.    187.02  sq.  ft.,   10.7  ft. 

Find  the  bases  of  pyramids  with  volumes  and  altitudes 
as  follows: 

5.    89.6  cu.  in.,  12.8  in.  6.    123.2  cu.  in.,  17.6  in. 

7.    178.2  cu.  in.,  19.8  in.  8.    140.4  cu.  in.,  23.4  in. 

9.  The  Great  Pyramid  in  Egypt  is  480}  ft.  high.  Its 
base  is  a  square,  764  ft.  on  a  side.  What  is  its  volume  ? 
If  it  weighs  168  lb.  per  cubic  foot,  what  is  its  weight? 


258 


MENSURATION 


283.  Volume  of  a  cone.    In  the  same  way  that  we  found 
the  volume  of  a  pyramid,  we  may 
find  that  of  a  cone. 

The  volume  of  a  cone  equals  one 
third  the  jproduct  of  its  base  and 
height. 

284.  If  the  base  is  circular,  as  is  commonly  the  case, 

V  =  ^  irr^h. 
It  is  desirable  that  these  solids  should  be  constructed  by  the  class. 

285.  Illustrative  problem.    What  is  the  volume  of  a  cone 
5  in.  high,  the  radius  of  the  base  being  2  in.  ? 

1.  The  area  of  the  base  =  irr'^  =  3.1416  x  4  sq.  in. 

2.  The  volume  =  i  x  5  x  3.1416  x  4  cu.  in.  =  20.944  cu.  in. 


WRITTEN   EXERCISE 

Find  the  volumes  of  cones,  given  the  radii  and  heights 
as  in  Exs,  i— ^,  using  tt  =  3^  m  all  the  exercises: 

1.    r  =  7.7  in.,  h  =  8.2  in.         2.    r  =  4.2  in.,  h  =  7.3  in. 
3.    r  =  6.3  in.,  h  =  9.8  in.        4.    r  =  11.9  in.,  h  =  5.7  in. 

5.  What  is  the  volume  of  a  cone  whose  altitude  is  18  in. 
and  the  circumference  of  whose  base  is  25i  in.  ? 

6.  A  water  tank  is  40  ft.  high  and  132  ft.  in  circumfer- 
ence.   What  is  its  capacity  in  cubic  feet  ?   in  gallons  ? 

7.  What  is  the  volume  of  a  cone  whose  altitude  equals 
the  diameter  of  the  base,  the  circumference  of  the  base 
being  44  in.? 

8.  The  interior  diameter  of  a  water  pipe  is  4  in.  The 
water  flows  through  at  the  rate  of  2  ft.  per  second.  How 
much  water  flows  through  in  a  minute  ? 


PYRAMID  AND  CONE 


259 


286.  Regular  pyramid.    If  the  sides  and  angles   of  the 
base  of  a  pyramid  are  respectively  equal,  and  the  vertex 
is  exactly  over  the  center  of  the  base,  the  y    . 
pyramid  is  said  to  be  regular, 

287.  Slant  height.  The  altitude  of  any  tri- 
angle forming  a  side  of  a  regular  pyramid  is 
called  the  slant  height  of  the  pyramid. 

VM  is  the  slant  height  of  the  pyramid  shown. 

288.  Surface  of  a  regular  pyramid.  Since  the  lateral  (side) 
surface  of  a  regular  pyramid  is  made  up  of  triangles,  each 
of  which  equals  half  the  base  times  the  altitude  (page  62), 
therefore 

The  lateral  area  of  a  regular  pyramid  equals  the  perimeter 
of  the  base  multiplied  by  half  of  the  slant  height. 

For  example,  if  AB  in  the  above  pyramid  is  5  ft.,  and  VM  is 
8  ft.,  the  lateral  area  is  4  x  5  x  4  sq.  ft.,  or  80  sq.  ft. 

289.  Surface  of  a  cone.  If  we  should  slit  the  surface  of 
this  common  form  of  cone,  often  called  a  right 
circular  cone,  and  flatten  it  out,  as  here  shown, 
we  should  have  part  of  a  circle.  In  the  same 
way  that  we  found  the  area  of  a  circle  (§  270) 
we  find  that 

^B       The  lateral  area  of  a  right  circular  cone  equals 
y  the  circumference  of  the  base  multiplied 

by  half  of  the  slant  height. 

For  example,  if  the  circumference  is 
10  ft.  and  the  slant  height  is  8  ft.,  the 
lateral  area  is  10  x  4  sq.  ft.,  or  40  sq.  ft. 
In  the  exercises  on  page  260  it  is  under, 
stood  that  regular  pyramids  and  right  circular  cones  are  given 
unless  the  contrary  is  stated. 


260  MENSURATION 


WRITTEN   EXERCISE 


Find  the  lateral  surfaces  of  regular  pyramids  with  the 
following  perimeters  of  bases  and  slant  heights: 

1.    16  in.,  4  in.  2.    32  in.,  17  in. 

3.    48  in.,  15  in.  4.    3  ft.  4  in.,  7  in. 

5.    2  ft.  8  in.,  11  in.  6.    6  ft.  7  in.,  15  in. 

Also  of  right  circular  cones  with  the  following .  circum- 
ferences and  slant  heights : 

7.    17.2  in.,  5|  in.  8.    16.5  in.,  4|  in. 

9.    14.9  in.,  2.8  in.  10.    6  ft.  8  in.,  1  yd. 

11.    3  ft.  4  in.,  17  in.  12.    2  ft.  7  in.,  19  in. 

13.  A  cone  lias  a  lateral  area  of  220  sq.  in.  The  radius 
of  the  base  is  7  in.    Find  the  slant  height. 

14.  A  pyramid  has  a  lateral  area  of  200  sq.  in.  The 
slant  height  is  8  in.    Find  the  perimeter  of  the  base. 

15.  A  conical  spire  has  a  slant  height  of  QtS  ft.  The- 
perimeter  of  the  base  is  60  ft.    What  is  the  lateral  surface  ?" 

16.  What  is  the  entire  area  of  a  cone,  including  the  base,, 
the  slant  height  of  which  is  7  ft.,  the  diameter  of  the  base 
being  7  ft.? 

17.  The  Great  Pyramid  of  Cheops  has  a  square  base 
764  ft.  on  a  side.  The  slant  height  is  about  500  ft.  About 
what  is  the  lateral  area  of  the  pyramid  ? 

18.  How  many  square  feet  should  be  allowed  for  slating 
a  steeple  in  the  form  of  a  regular  pyramid  of  slant  height 
40  ft.,  the  perimeter  of  the  base  being  48  ft.  ? 

19.  A  dome  is  surmounted  by  a  gilded  cone  whose  slant 
height  is  16  ft.  8  in.,  the  radius  of  the  base  being  3  ft.  6  in. 
How  many  square  feet  must  be  allowed  for  gilding?' 


SURFACE  OF  A  SPHERE 


261 


290.  Surface  of  a  sphere.    If  we  wind  a  sphere  with  cord, 
and  wind  a  cylinder  whose  radius  equals  the  radius  of  the 


sphere,  and  whose  height  equals  the  diameter,  we  find  that 
it  takes  as  much  cord  for  the  cylinder  as  for  the  sphere. 

In  the  picture,  for  convenience,  only  half  of  each  is  wound. 

Therefore  the  surface  of  a  sphere  equals  the  curved  sur- 
face of  a  cylinder  of  the  same  radius  and  height. 

291.  Formula  for  area  of  the  sphere.    Since  the  curved  sur- 
face of  the  cylinder  is  2  7rr  x  h,  where  A  =  2  r,  therefore 

area  of  sphere  =  2  7rrx2r  =  4 7rr^. 

292.  Illustrative  problem.    If   the   earth   is   a  sphere  of 
4000  mi.  radius,  what  is  its  area? 

1.  40002  =  16,000,000. 

2.  4  7r  X  16,000,000  =  4  x  3}  x  16,000,000  =  201,142,857f 

3.  Therefore  the  area' is  about  201,143,000  sq.  mi. 


WRITTEN   EXERCISE 

1.  If  a  ball  has  a  radius  of  2\  in.,  what  is  its  area? 

2.  The  sun's  diameter  is  866,500  mi.    Find  its  area. 

3.  If  a  tennis  ball  is  2|  in.  in  diatneter,  what  is  its  area  ? 

4.  A  gilded  ball  is  to  be  put  on  top  of  a  tower.  The 
diameter  of  the  ball  is  2'  6".  How  many  square  inches  are 
to  be  gilded,  making  no  allowance  for  the  support  ? 


262 


MENSURATION 


293.  Sphere  and  cylinder  compared.    If  we  place  this  sphere 
in  this  cylinder  of  the  same  diameter  and  height,  and  fill 


in  the  spaces  with  sand,  the  sand  will  fill  one  third  of  the 
cylinder  when  the  sphere  is  removed.     Therefore 

A  sphere  equals  tivo  thirds  of  a  cylinder  of  the  same  diam- 
eter and  height. 

294.  Volume  of  a  sphere.  And  since  the  volume  of  the 
cylinder  is  7rr^  X  2  r,  or  2  tt?*^  (§  278),  and  the  sphere 
is  f  as  large,  or  |  of  2  irr^, 

The  volume  of  a  sphere  is  f  irr^. 

295.  Illustrative  problem.  What  is  the  volume  of  a  sphere 
whose  radius  is  21  in.  ? 


^4x22x^;x21x21^3 
3x7 
Therefore  the  volume  is  38,808  cu.  in. 
In  the  following  examples  and  on  pages  263,  264,  use  tt  =  3i. 


WRITTEN  EXERCISE 

What  are  the  volumes  of  spheres  with  radii  as  follows  f 
1.  2|".       2.10.5".       3.  1000  mi.       4.  7' 6".       5.  9' 7". 
Also  with  diameters  as  follows? 
6.  3' 6".     7.  4' 8".        8.  8000  mi.       9.9.6'.       10.11.4'. 


REVIEW  263 

Find  the  areas  of  the  squares  whose  sides  are  as  follows: 
/\\,    II  in.  12.    If  in.  13.    1 7  in.  14.    J|  in. 

15.    2.87  ft.       16.    3.92  ft.       17.    17.5  rd.      18.    0.37  in. 
Find  the  areas  of  the  rectangles  whose  dimensions  are : 
19.    3.4  ft.,  9.2  ft.  20.    6.4  in.,  7.3  in. 

21.    11  yd.,  27^  in.  22.   4.1  ft.,  11.3  in. 

23. '  4.92  in.,  0.97  in.  24.    14  ft.  3  in.,  2  ft.  8  in. 

Find  the  areas  of  the  triangles  whose  bases  and  altitudes 
are  respectively  as  follows: 

25.    4.7  ft.,  3.8  ft.  26.    6i  yd.,  27  in. 

27.    0.37  in.,  0.42  in.  28.    6.4  in.,  4.9  in. 

29.    4^  yd.,  3  ft.  9  in.  30.    Q>.S  ft.,  11.9  in. 

Griven  rectangles  with  areas  and  lengths  as  follows^  to 
find  the  widths: 

31.    306  sq.  in.,  17  in.  32.    90.3  sq.  in.,  43  in. 

33.    14.62  sq.  in.,  4.3  in.  34.    4.18  sq.  in.,  2.2  in. 

.  35.    473  sq.  in.,  3  ft.  7  in.         36.    850  sq.  in.,  4  ft.  2  in. 

Griven  triangles  with  areas  and  bases  as  follows^  to  find 
the  altitudes: 

37.    864  sq.  in.,  27  in.  38.    14.72  sq.  ft.,  4.6  ft. 

39.    101.4  sq.  in.,  26  in.  40.    25.62  sq.  in.,  6.1  in. 

41.    0.0704  sq.  in.,  0.32  in.       42.    2911  sq.  in.,  3  ft.  5  in. 

Find  the  sides  of  the  squares  whose  areas  are  given  in 
Exs.  If3-61^  carrying  the  results  to  two  decimal  places : 
43.    2  A.  44.    171  sq.  ft.  45.    385  sq.  ft. 

46.    153  sq.  in.  47.    352  sq.  rd.         48.    251  sq.  yd. 

49.    7.52  sq.  in.         50.    6.04  sq.  yd.        51.    8.51  sq.  in. 


264  MENSURATION 

Find  the  areas  of  the  circles  whose  radii  are  : 
52.    14  in.  53.    15.4  in.  54.    39.9  in. 

55.    64.4  ft.  56.    71.4  ft.  57.    92.4  yd. 

58.    123.9  rd.  59.    164.5  rd.  60.    235.9  yd. 

Find  the  radii  of  the  circles  whose  areas  are  : 
61.    308  sq.  in.         62.    770  sq.  in.         63.    1386  sq.  in. 
64.    1694  sq.  ft.       65.    1848  sq.  ft.       66.    2618  sq.  ft. 
67.    40.04  sq.  yd.     68.    44.77  sq.  yd.     69.    141.68  sq.  yd. 

Find  the  volumes  and  surfaces  of  the  spheres  whose 
radii  are  as  follows: 

70.    181  in.  71.    172  in.  72.    625  in. 

73.    31.8  in.  74.    27.6  in.  75.   34.2  in. 

Find  the  volumes  of  the  pyramids  whose  bases  and  alti- 
tudes are  respectively : 

76.    21.6  sq.  ft.,  3  ft.  77.    16.4  sq.  in.,  17.1  in. 

78.    17.4  sq.  in.,  12.3  in.         79.   26.2  sq.  ft.,  5  ft.  1  in. 

Find  the  volumes  of  the  cylinders  whose  altitudes  and 
the  radii  of  whose  bases  are  respectively  : 

80.    2.8  ft.,  1.7  ft.  81.    2.7  in.,  7.2  in. 

82.    6.2  in.,  3.4  in.  83.    14.2  ft.,  8.1  ft. 

Find  the  volumes  of  the  cones  whose  altitudes  and  the 
radii  of  whose  bases  are  respectively : 

84.    6.2  ft.,  4.1  ft.  85.    3.9  ft.,  2.4  ft. 

86.    3.4  in.,  4.2  in.  87.    6.7  in.,  7.8  in. 

88.    2.8  in.,  3.1  in.  89.    12.8  ft.,  6.1  ft. 

90.    4  ft.  7  in.,  2  ft.  1  in.        91.    6  ft.  8  in.,  3  ft.  2  in. 


REVIEW  265 

"^      92.    If  a  cubic  foot  of  granite  weighs  165  lb.,  what  is  the 
weight  of  a  sphere  of  granite  1  ft.  in  diameter? 

93.  How  many  tons  of  water  will  fill  a  tank  14  ft.  by 
8  ft.  by  8  ft.,  allowing  1000  oz.  to  a  cubic  foot  ? 

94.  A  bowl  is  in  the  form  of  a  hemisphere  4.2  in.  in 
diameter.    How  many  cubic  inches  does  it  contain? 

95.  If  a  cubic  foot  of  marble  weighs  173  lb.,  what  is  the 
weight  of  a  cylindrical  marble  column  10  ft.  high  and  16  in. 
in  diameter? 

96.  How  many  loads  (cubic  yards)  of  earth  must  be 
removed  in  digging  a  canal  2  mi.  1740  ft.  long,  200  ft.  wide, 
and  16  ft.  deep? 

97.  In  a  cylindrical  jar  4  in.  high  and  3  in.  in  diameter, 
half  full  of  water,  a  marble  1  in.  in  diameter  is  dropped. 
It  causes  the  water  to  rise  how  much  ? 

98.  What  is  the  weight  of  a  sphere  of  steel  7  in.  in 
diameter,  steel  being  7.8  times  as  heavy  as  water,  and 
1  cu.  ft.  of  water  weighing  1000  oz.  ? 

99.  What  is  the  weight  of  a  sphere  of  marble  3  ft.  in 
circumference,  marble  being  2.7  times  as  heavy  as  water, 
1  cu.  ft.  of  water  weighing  1000  oz.  ? 

100.  The  entire  surface  of  a  pyramid  is  made  up  of  four 
equal-sided  triangles  3  ft.  on  a  side.  What  is  the  total 
area?    (Carry  the  result  to  hundredths.) 

101.  The  diameter  of  a  sphere  and  the  altitude  of  a  cone 
are  equal,  and  they  have  equal  radii.  The  volume  of  the 
sphere  is  how  many  times  that  of  the  cone? 

102.  Taking  the  radius  of  the  earth  as  4000  mi.,  and  the 
earth  as  an  exact  sphere,  what  is  its  volume  ?  How  many 
square  miles  on  its  surface?  (Carry  the  answers  only  to 
1000  square  or  cubic  miles.) 


266  MISCELLANEOUS  PROBLEMS 

MISCELLANEOUS  PROBLEMS 

296.  Nature  of  the  problems.  The  following  list  contains 
certain  problems  whose  interest  is  rather  in  the  reasoning 
exercised  in  solution  than  in  their  applicability  to  the  life 
of  to-day. 

WRITTEN   EXERCISE 

1.  Divide  91  into  two  parts  having  the  ratio  of  5  :  8. 

2.  The  product  of  two  numbers  is  175  and  their  quotient 
is  7.    What  are  the  numbers? 

3.  How  many  bananas  are  there  in  a  bunch  of  which 
7  are  decayed  and  95%  are  not? 

4.  The  sum  of  two  numbers  is  783  and  their  difference 
is  191.    What  are  the  numbers? 

5.  At  200  lb.  per  cubic  foot,  what  is  the  weight  of  a 
block  of  stone  4'3i"  x  1'  1"  X  9.6"? 

6.  At  $1.95  a  rod,  how  much  will  it  cost  to  fence  a 
rectangular  2-acre  field  that  is  5  ch.  long? 

7.  If  iron  weighs  444.56  lb.  per  cubic  foot,   find  the 
weight  of  a  14-ft.  bar  of  2"  x  1^"  iron. 

8.  How  much  is  gained  by  buying  63  gal.  of  molasses 
for  $25.20  and  selling  it  at  12/  a  quart? 

9.  What  is  the  rate  of  gain  when  oranges  are  bought 
at  40  for  $1,  and  sold  at  50/  a  dozen  ? 

10.  What  is  the  rate  of  gain  when  eggs  are  bought  at  16 
for  a  quarter  and  sold  at  13  for  a  quarter? 

11.  What  is  the  height  of  a  block  of  marble  4'  2"  x  2'  1'', 
that  weighs  as  much  as  one  3'  4"  x  2'  1"  x  2'  5"? 

12.  A  man  owns  100  A.  of  coal  land,  the  coal  bed  being 
11  ft.  thick.  Allowing  35  cu.  ft.  to  the  ton,  how  many  tons 
of  coal  in  the  bed? 


MISCELLANEOUS  PROBLEMS  267 

13.  The  minute  hand  of  my  watch  is  /^  in.  long.  Over 
what  area  does  it  pass  in  a  day? 

14.  If  15  horses  eat  11  bu.  of  oats  in  9  da.,  how  long 
will  44  bu.  last  45  horses  at  the  same  rate? 

15.  In  the  year  when  Michigan  produced  11,135,215  long 
tons  of  iron,  how  many  pounds  did  it  produce? 

16.  If  telegraph  poles  are  198  ft.  apart,  and  a  train  passes 
one  every  3  sec,  what  is  the  train's  rate  per  hour  ? 

17.  The  pitch  of  a  screw  is  16  threads  to  the  inch.  How 
many  turns  must  be  made  to  move  the  screw  |  in.  ? 

18.  A  dealer  bought  hay  at  $8.66  a  ton  and  sold  it  at 
$9.75,  gaining  $408.75.    How  many  tons  did  he  buy  ? 

19.  What  will  it  cost  to  fill  in  3  acres  of  swamp  land, 
raising  the  level  on  an  average  of  5  ft.,  at  45/  a  load? 

20.  A  man  used  a  bicycle  for  a  month  and  sold  it  15% 
below  cost,  receiving  $29.75  for  it.    How  much  did  he  lose? 

21.  What  is  the  list  price  of  some  goods  which  cost 
$68.40  after  the  discounts  10%,  5%  have  been  deducted? 

22.  At  what  price  must  a  dealer  mark  goods  that  cost 
him  $450  so  as  to  take  off  10%  and  still  make  10%  profit? 

23.  What  is  the  shortest  distance  that  can  be  measured 
exactly  by  a  yardstick,  a  fathom  rod,  or  a  pole  1  rd.  long? 

24.  A  man  sold  two  carriages  at  $150  each.  On  one  he 
gained  20%,  and  on  the  other  he  lost  20%.  Did  he  gain  or 
lose  on  both,  and  how  much  ? 

25.  A  man  bought  a  horse  for  $95  and  sold  it  for  $114. 
What  was  his  gain  per  cent?  The  purchaser  sold  the  horse 
for  $95.    What  was  his  loss  per  cent? 

26.  In  the  year  when  Michigan  produced  7,729,808  barrels 
of  salt,  this  was  37.6%  of  the  total  amount  produced  in 
the  United  States.    How  many  were  produced  in  all? 


268  MISCELLANEOUS  PROBLEMS 

27.  At  what  distance  from  the  end  must  a  piece  of  tim- 
ber 16"  square  be  sawed  so  as  to  cut  off  9  cu.  ft.  ? 

28.  Around  a  circular  flower  bed  28  ft.  in  diameter  is  a 
gravel  walk  7  ft.  wide.    What  is  the  area  of  the  walk? 

29.  If  6  men  can  do  a  piece  of  work  in  4  da.,  how  many 
more  must  be  employed  to  finish  the  work  one  day  sooner  ? 

30.  A  man  can  mow  f  of  a  field  in  If  hr.  How  many 
hours  will  it  take  to  mow  the  whole  field  at  this  rate? 

31.  If  84  men  can  do  a  piece  of  work  in  2  mo.,  how  long 
will  it  take  12  men  to  do  the  same  work  at  the  same  rate  ? 

32.  A  train  156  ft.  long  is  traveling  60  mi.  an  hour.  How 
long  will  it  take  it  to  completely  cross  a  bridge  295  ft.  long  ? 

33.  One  man  can  do  a  piece  of  work  in  4  da.  which 
another  can  do  in  5  da.  At  these  rates,  how  long  will  it 
take  them  to  do  the  work,  together? 

The  first  does  what  part  in  one  day?  The  second  does  what 
part  in  one  day  ?  Together  they  do  what  part  in  one  day  ?  How 
many  days  will  it  take  them? 

34.  A  boy,  after  doing  |  of  a  piece  of  work  in  30  days, 
is  assisted  by  a  man,  with  whom  he  completes  it  in  6  days. 
How  long  would  it  take  each  to  do  the  work  alone? 

35.  If  a  certain  number  of  men  can  do  a  piece  of  work 
in  15  da.,  how  long  will  it  take  if  twice  as  many  men  are 
added  to  this  number? 

36.  If  19  men  can  do  a  piece  of  work  in  76  da.  of  7  hr. 
each,  how  many  men,  working  at  the  same  rate,  will  it  take 
to  do  the  work  in  133  hr.  ? 

37.  An  expert  typesetter,  working  by  the  hour,  receives 
$32.40  a  week,  working  9  hr.  daily  except  Sunday.  How 
many  hours  a  day  must  he  work  to  earn  $19.20  in  4  da. 
at  the  same  rate? 


MISCELLANEOUS  PROBLEMS  269 

38.  What  two  equal  numbers  produce,  when  multiplied 
together,  15,129? 

39.  The  square  root  of  a  certain  number  is  42.3.  What 
is  42.3%  of  the  number? 

40.  A  square  is  300  ft.  on  a  side.  How  long  is  the 
diagonal?    Answer  to  two  decimal  places. 

41.  Multiply  the  square  root  of  13.7641  by  the  sum  of 
2.06  and  1.65,  and  extract  the  square  root  of  the  product. 

42.  A  51-ft.  ladder  rests  against  a  building,  its  foot  being 
24  ft.  from  the  wall.    How  high  does  it  reach? 

43.  How  long  is  a  ladder  that  just  reaches  the  top  of  a 
4-story  building,  averaging  10  ft.  to  a  story,  the  foot  of  the 
ladder  being  9  ft.  from  the  wall? 

44.  From  the  top  of  a  24-ft.  flagstaff  a  rope  is  stretched 
to  a  point  7  ft.  from  the  foot  of  the  staff.  How  long  is  the 
rope? 

45.  A  baseball  "  diamond  "  is  a  square  90  ft.  on  a  side. 
How  far  must  the  second  baseman  throw  from  his  base  to 
the  home  plate  ?    Answer  to  two  decimal  places. 

46.  How  far  must  the  catcher  throw  from  the  home  plate 
to  the  shortstop,  who  stands  halfway  between  the  second 
and  third  bases  of  a  baseball  diamond  ?  Answer  to  two 
decimal  places.    (See  Ex.  45.) 

47.  If  a  locomotive  travels  90  mi.  in  2  hr.,  the  piston 
making  162  strokes  a  minute,  how  many  strokes  per  minute 
must  be  made  for  the  same  locomotive  to  travel  200  mi. 
in  4^  hr.  ? 

48.  A  city  newspaper  office  must  get  out  an  edition  of 
126,000  papers.  It  has  two  presses,  each  with  a  capacity 
of  300  papers  a  minute.  How  long  will  it  take  to  print 
the  edition? 


270  MISCELLANEOUS  PROBLEMS 

49.  How  many  steps  of  2  ft.  9  in.  each  would  you  have 
to  take  in  a  minute  in  order  to  walk  at  the  rate  of  4  mi. 
per  hour? 

50.  At  the  rate  of  f  cu.  yd.  of  earth  in  15  min.,  how  long 
would  it  take  a  man  to  excavate  a  cellar  15  ft.  square  and 
7^  ft.  deep? 

51.  A  machine  does  a  certain  amount  of  work  in  12  hr. 
If  its  capacity  be  increased  20%,  how  long  will  it  take  it 
to  do  the  work  ? 

52.  Of  three  partners,  one  is  entitled  to  y\  and  another  to 
•^-g  of  the  profits.  If  they  make  $4500,  what  is  the  share 
of  each  of  the  three? 

53.  If  a  certain  gun  metal  is  composed  of  16%  tin  and 
the  rest  copper,  how  many  pounds  of  tin  will  be  needed 
with  46.2  lb.  of  copper  ? 

54.  Two  cans  have  a  capacity  of  7  pt.  and  10  pt.  respec- 
tively. How  would  you  measure  out  16  pt.  into  a  third 
can  by  using  these  alone? 

55.  A  dealer  marked  a  bedroom  set  15%  above  cost,  this 
representing  a  gain  of  $9.30.  He  sold  it  at  a  discount  of 
10%.    How  much  did  he  gain? 

56.  A  strip  of  carpet  50  yd.  long  and  27  in.  wide  weighs 
200  lb.  What  is  the  weight  of  such  a  carpet  covering  an 
assembly  room  135  ft.  x  150  ft.  ? 

57.  If  a  gallon  of  water  weighs  10  lb.,  and  a  cubic  foot 
of  water  weighs  1000  oz.,  how  many  gallons  are  there  in  a 
cistern  which  contains  16  cu.  ft.  ? 

58.  A  man  bought  a  piece  of  alloy  for  $72.25.  The 
number  of  pounds  purchased  and  the  number  of  dollars 
per  pound  were  the  same.  How  many  pounds  did  he 
purchase  ?  ^ 


/ 


MISCELLANEOUS  PROBLEMS  271 

59.  What  is  the  number  which  multiplied  by  80%  of 
itself  equals  4500? 

69.  The  diagonal  of  one  face  of  a  cube  is  Vl62  in.  Find 
the  surface  and  the  volume  of  the  cube. 

61.  A  horse  is  tied  to  a  corner  post  of  a  square  field  by 
a  rope  35  ft.  long.    Over  what  part  of  an  acre  can  he  feed? 

62.  If  a  horse  is  tethered  by  a  30-ft.  rope,  it  can  graze 
over  how  many  times  as  much  ground  as  it  could  if  the 
rope  were  only  20  ft.  long  ? 

63.  What  is  the  area  of  the  largest  circle  that  can  be 
inscribed  in  a  square  whose  area  is  196  sq.  in.?  of  the 
largest  square  that  can  be  inscribed  in  the  circle? 

64.  A  locomotive  wheel  5  ft.  in  diameter  makes  300  revo- 
lutions a  minute,  and  travels  at  this  rate  for  4  hr.  10  min. 
without  stopping.    How  far  does  it  go  ?  (Take  ir  =  3|.) 

65.  A  wheel  7  ft.  8  in.  in  circumference  revolves  3762 
times  in  going  a  certain  distance.  Another  wheel  revolves 
3496  times  in  going  the  same  distance.  What  is  the  cir- 
cumference of  the  latter? 

66.  A  piece  of  brickwork  279  ft.  long  is  completed  in  21 
days.  At  this  rate,  how  long  would  it  take  to  complete  a 
piece  twice  as  high  and  651  ft.  long? 

67.  A  boy  buys  apples  at  the  rate  of  5  for  2  ct.,  and  sells 
them  at  the  rate  of  8  ct.  a  dozen.  How  many  apples  must 
he  buy  and  sell  in  order  to  gain  $2? 

68.  The  equatorial  diameter  of  the  earth  is  estimated 
at  20,926,202  ft.,  and  the  polar  diameter  at  20,854,895  ft. 
Express  each  in  miles  and  find  the  difference. 

69.  A,  B,  and  C  bought  a  horse  for  $112  and  sold  it  at  a 
profit  of  25%,  by  which  A  gained  $6  and  C  twice  as  much. 
How  much  did  each  of  the  three  pay  for  the  horse? 


272  MISCELLANEOUS  PROBLEMS 

70.  How  many  acres  in  a  square  field  whose  diagonal  is 
120  rd.? 

71.  What  is  the  square  root  of  J  of  the  product  of  the 
square  root  and  the  cube  root  of  729? 

72.  If  145  bu.  of  turnips  last  53  oxen  a  fortnight,  how 
long  will  435  bu.  last  371  oxen  ? 

73.  A  man  computing  the  cost  of  43  articles  multiplied, 
by  mistake,  the  cost  of  each  by  34  instead  of  43  and  obtained 
$84.32.    What  was  the  correct  cost  of  the  lot? 

74.  Two  masts  of  a  ship  are  45  ft.  6  in.  apart,  one  being 
60  ft.  high  and  the  other  70  ft.  Supposing  them  perpen- 
dicular to  the  deck,  how  far  is  it  from  the  top  of  one  mast 
directly  to  the  top  of  the  other?    (Two  decimals.) 

75.  Add  f ,  I,  I,  and  f .  Keduce  the  result  to  a  decimal 
fraction,  to  three  decimal  places.  Also  reduce  each  of  the 
addends  to  a  decimal  fraction  carried  to  four  places,  and  add. 

76.  One  man  can  do  J  of  a  piece  of  work  in  a  day,  and 
another  can  do  66|%  as  much.  How  long  will  it  take  them, 
working  together,  to  do  the  whole  work? 

77.  Two  ships,  sailing  in  opposite  directions,  pass  in 
mid-ocean.  One  averages  7°  30'  a  day,  and  the  other  75% 
as  much.  What  is  their  difference  in  ship  time  exactly 
4  da.  after  passing? 

78.  In  closing  out  a  line  of  goods  a  merchant  asked  20% 
less  than  a  certain  article  cost,  but  at  an  auction  sale  he  suc- 
ceeded in  getting  20%  more  than  this  asking  price.  What 
per  cent  did  he  lose  on  the  cost? 

79.  If  Michigan,  one  of  the  largest  producers  of  Portland 
cement,  made  1,602,370  bbl.  in  a  certain  year,  an  increase 
of  10%  on  the  preceding  year,  how  many  barrels  were 
produced  in  the  preceding  year? 


MISCELLANEOUS  PROBLEMS  273 

80.  Water  is  flowing  into  a  tank  whose  base  measure  is 
4'  4"  X  2'  7"  at  the  rate  of  0.62  cu.  ft.  in  3  min.  How  long 
will  it  take  the  water  to  fill  it  to  a  depth  of  2'  8"? 

81.  A  12-in.  gun  can  fire  a  shell  weighing  850  lb.  every 
30  sec.  At  this  rate,  how  many  pounds  of  shell  could  a 
battle  ship  fire  from  four  12-in.  guns  in  2  min.? 

82.  A  train  leaves  a  city  at  5:15  p.m.,  and  reaches  a  city 
109-|-  mi.  distant  at  7:51  p.m.  Allowing  10  min.  for  stop- 
ping at  stations,  what  is  the  rate  of  travel  per  hour  ? 

83.  The  .greatest  known  depth  of  the  ocean  is  5000 
fathoms,  and  the  greatest  mountain  height  is  29,002  ft. 
Find  the  difference  in  level,  in  miles,  to  three  decimal  places. 

84.  A  square  park  is  surrounded  by  a  gravel  walk  7'  6" 
wide.  The  park  and  walk  together  contain  1.6  acres.  Find 
the  cost  of  making  the  gravel  walk  at  10/  per  square  yard. 

85.  A  grocer  bought  400  bunches  of  lettuce  for  $8.  He 
sold  all  but  43  heads  at  5/  each.  Of  the  43  heads  he  sold 
30  at  1/  each  and  the  rest  he  threw  away.  How  much  did 
he  gain? 

86.  The  product  of  two  numbers  is  48  less  than  half 
the  number  of  feet  in  a  mile,  and  one  of  the  numbers  is 
the  number  of  cubic  inches  in  a  cubic  foot.  What  is  the 
other  number? 

87.  A  farmer  finds  that  a  bin  8  ft.  long,  3  ft.  6  in.  wide, 
and  5  ft.  deep  holds  112  bu.  How  many  bushels  will  be 
contained  in  a  bin  50%  longer,  twice  as  wide,  and  of  the 
same  depth? 

88.  How  much  must  the  terms  of  the  fraction  ||J  be 
increased  to  make  the  fraction  equal  f|?  decreased  to 
make  the  fraction  equal  ^^?  increased  to  make  the  frac- 
tion equal  f  |  ? 


274  MISCELLANEOUS  PROBLEMS 

89.  If  6  men  can  lay  the  tiles  in  a  large  railway  station 
in  16  da.,  how  many  men  must  be  added  to  the  job  to  com- 
plete it  4  da.  sooner? 

90.  How  many  times  will  a  locomotive  drive  wheel  5  ft. 
10  in.  in  diameter  revolve  in  going  from  'New  York  to 
Chicago,  a  distance  of  983  mi.? 

91.  A  man  deposited  some  money  in  the  bank,  and  then 
drew  out  15%  of  the  amount,  then  20%  of  the  remainder, 
and  then  30%  of  what  was  still  left,  and  there  then  remained 
$809.20.    What  was  the  deposit? 

92.  If  the  area  of  Illinois  is  56,650  sq.  mi.,  and  if  in  a 
certain  year  91.5%  of  the  area  was  included  in  farms,  and 
84.5%  of  this  part  was  improved  farm  land,  how  many  acres 
of  improved  farm  land  were  there? 

93.  When  Adams  County,  Illinois,  had  a  population  of 
67, 100,  Lasalle  County  had  a  population  31  %  larger,  and  Cook 
County  had  1200%  as  much  as  both  these  counties  together. 
What  was  then  the  population  of  Cook  County? 

94.  When  Port  Arthur  was  captured  it  was  found  that 
there  was  food  enough  for  the  45,000  soldiers  and  inhab- 
itants for  6  wk.  Suppose  there  had  been  9000  more  men, 
for  how  long  would  the  food  have  been  sufficient? 

95.  A  village  has  a  water  tank  42  ft.  in  diameter.  In 
7  hr.  30  min.,  when  no  water  is  being  pumped  in,  the  water 
is  lowered  6  ft.  How  many  gallons  are  drawn  out  on  an 
average  each  hour  of  this  period?    (Use  7.6  gal.  to  1  cu.  ft.) 

96.  When  the  manufactured  products  of  Illinois  were  a 
billion  and  a  quarter  dollars  a  year,  the  only  states  with  a 
larger  product  were  Kew  York,  with  75%  more,  and  Pennsyl- 
vania, with  48  %  more.  The  manufactures  of  New  York  then 
exceeded  those  of  Pennsylvania  by  what  per  cent? 


MISCELLANEOUS  PROBLEMS  275 

97.  A  rug-cleaning  establishment  charges  12/  a  yard  for 
cleaning  carpets  27  in.  wide.  At  the  same  rate  per  square 
yard,  how  much  will  it  charge  for  cleaning  two  rugs  7'  6"  x 
5' 6"  and  5' X  8' 6"? 

98.  A  grain  of  gold  can  be  beaten  out  into  a  leaf  of 
56  sq.  in.  How  many  of  these  leaves,  pressed  one  upon 
another,  would  make  a  pile  1  in.  high,  1  cu.  in.  of  gold 
weighing  10  troy  ounces? 

99.  The  quotient  of  two  numbers  is  the  sum  of  the 
numbers  denoting  the  length  of  a  mile  expressed  in  feet 
and  the  length  of  a  rod  expressed  in  feet.  The  dividend  is 
21,186.    What  is  the  divisor? 

100.  A  certain  university  library  increases  at  the  rate 
of  18,000  books  a  year.  Allowing  300  working  days  to  the 
year,  and  10  hours  to  the  day,  how  often,  on  an  average, 
does  a  new  book  come  to  the  library  ? 

101.  If  3i^  bbl.  of  lime  are  required  for  plastering  100 
sq.  yd.,  how  many  barrels  will  be  required  for  a  job  of 
plastering  equivalent  to  a  wall  surface  231'  x  9'?  How 
many  for  6831  sq.  ft.  ? 

102.  For  a  cellar  floor  153  cu.  ft.  of  concrete  are  needed. 
To  make  this  there  are  used  2  parts  of  fresh  powdered  lime, 
1  part  of  Portland  cement,  6  parts  of  gravel.  How  many 
cubic  feet  of  each  are  used? 

103.  If  it  takes  1  bbl.  of  lime  and  f  cu.  yd.  of  sand  to 
make  the  mortar  for  1000  bricks,  and  if  22^  bricks  are 
allowed  per  cubic  foot  of  wall,  how  much  lime  and  sand 
are  needed  for  a  wall  30'  x  10'  x  1'  6"? 

104.  If  the  more  liberal  estimate  of  23  bricks  to  1  cu.  ft. 
is  allowed,  how  many  bricks  would  be  needed  for  a  wall 
50'  X  100'  X  20"? 


276  MISCELLANEOUS  PROBLEMS 

105.  A  boy  who  can  swim  1  yd.  a  second  swims  down- 
stream for  10  minutes,  the  stream  flowing  15  yd.  a  minute. 
How  far  does  he  go?  At  the  same  rates,  how  long  will  it 
take  him  to  swim  back  to  where  he  started? 

106.  I  paid  a  bookseller  $5.05  for  three  books,  a  history, 
an  atlas,  and  a  dictionary.  The  history  and  atlas  together 
cost  $2.85,  and  the  atlas  and  dictionary  together  $3.80. 
What  was  the  price  of  each? 

107.  A  tank  8'  x  3'  x  9"  is  filled  with  pulp  for  making 
paper.  How  long  a  strip  of  paper,  2'  6"  wide,  can  be  made 
from  this  pulp,  the  paper  being  gj  o  ^^-  thick,  and  half  the 
volume  of  the  pulp  being  lost  in  drying  and  rolling? 

108.  Two  persons  start  at  the  same  time  from  places 
6^  mi.  apart,  and  go  towards  each  other.  One  walks  at  the 
rate  of  3  mi.  an  hour,  and  the  other  goes  in  an  automobile 
at  the  rate  of  10  mi.  an  hour.  When  and  where  will  they 
meet? 

109.  A  druggist  has  his  clerk  prepare  200  boxes  of  salve, 
the  material  costing  $4.90,  the  boxes  $2.20,  the  labels  $2, 
and  the  time  of  the  clerk  being  worth  $3.  He  sells  the 
salve  at  15/  per  box.  How  much  does  he  gain  by  the 
transaction  ? 

110.  Two  water  filters  discharge  into  the  same  jar,  one 
at  the  rate  of  16  qt.  an  hour,  the  other  at  the  rate  of  3J  qt. 
every  15  min.  What  is  the  capacity  of  the  smallest  jar 
that  can  be  filled  in  an  integral  number  of  minutes  by 
either  filter? 

'  111.  A  man  wishes  to  go  from  one  corner  of  a  rectangular 
field  60  rd.  long  and  11  rd.  wide,  to  the  diagonally  opposite 
corner.  How  many  steps  will  he  save  by  going  directly  across 
the  field,  instead  of  going  along  the  two  sides,  allowing 
2  ft.  6  in.  to  a  step? 


MISCELLANEOUS  PROBLEMS  277 

112.  An  ice  company  has  an  ice  house  120  ft.  long,  52  ft. 
wide,  and  28  ft.  high,  after  making  allowance  for  packing. 
How  many  tons  of  ice  will  it  hold,  allowing  58j  lb.  to  the 
cubic  foot? 

113.  How  many  croquet  balls  3  in.  in  diameter  can  be 
placed  in  a  cubical  can  whose  interior  height  is  2  ft.  3  in.  ? 
How  many  quarts  of  water  can  be  poured  in  after  the  balls 
are  in  place  ? 

114.  At  the  time  that  Illinois  had  11,427  miles  of  railway 
track  it  had  more  than  any  other  state.  If  the  weight  of 
a  rail  averaged  80  lb.  to  the  yard,  how  many  tons  of  steel 
were  used  for  the  Illinois  roads? 

115.  Two  men  rent  an  automobile  for  fifteen  weeks 
during  the  summer  season.  One  uses  it  7  wk.,  and  the 
other  8  wk.  If  they  pay  $345  rent,  what  is  the  share 
of  each? 

116.  Three  men  own  lots  having  frontages  of  35  ft., 
40  ft.,  and  50  ft.,  respectively,  on  the  same  street.  They 
are  assessed  $150  for  street  improvement.  If  assessed 
according  to  the  frontage,  what  should  each  pay? 

117.  Two  houses  rent  for  $300  a  year,  the  rent  being 
paid  monthly  in  advance  in  one  case,  and  at  the  end  of 
each  quarter  (3  mo.)  in  the  other.  What  is  the  difference 
in  the  amount  of  each  rent  in  2  yr.,  allowing  6%  simple 
interest? 

118.  Three  men  own  adjoining  land  fronting  on  the 
same  street,  the  frontages  being  561  ft.,  357  ft.,  and  459  ft. 
respectively.  They  agree  to  cut  each  piece  into  building 
lots,  and  they  wish  all  the  lots  to  have  the  same  frontage. 
What  is  the  greatest  possible  frontage  of  each,  and  how 
many  lots  will  each  man  have? 


278  MISCELLANEOUS  PROBLEMS 

119.  At  what  time  between  1  and  2  o'clock  will  the  hands 
of  a  clock  be  together  ? 

Looking  at  the  clock,  it  is  evident  that  they  are  together  at  12. 
We  may  also  think  of  the  hour  hand  as  60  minute  spaces  ahead 
of  the  minute  hand  at  that  time,  so  that  the  minute  hand  must 
gain  60  minute  spaces  to  overtake  the  hour  hand  again.  But  in 
1  hr.  it  evidently  gains  only  55  minute  spaces,  for  at  1  o'clock  the 
hour  hand  is  5  minute  spaces  ahead.  Since  it  gains  55  in  1  hr., 
to  gain  60  it  will  take  f^  hr.,  or  Ij^  hr.,  or  1  hr.  5  min.  27^^  sec. 
(Draw^the  face  of  a  clock  to  illustrate  this.) 

At  what  time  between  2  and  3  o'clock  will  they  be  together  ? 

120.  At  what  time  will  the  hands  of  a  clock  be  together 
between  4  and  5  o'clock?  between  7  and  8  o'clock? 

121.  At  what  times  between  2  and  3  o'clock  will  the  hour 
and  minute  hands  be  at  right  angles  ? 

From  noon  the  minute  hand  would  have  to  gain  on  the  hour 
hand  120  minute  spaces  for  the  two  to  be  together,  or  120  +  15 
or  120  +  45  for  them  to  be  at  right  angles. 

122.  At  what  times  between  5  and  6  o'clock  will  the  hour 
and  minute  hands  of  a  clock  be  at  right  angles  ?  together  ? 

123.  At  what  times  between  9  and  10  o'clock  will  the 
hour  and  minute  hands  of  a  clock  make  with  each  other 
an  angle  of  120°? 

124.  If  a  clock  is  2  min.  30  sec.  fast  at  noon,  January  1, 
and  gains  3  min.  30  sec.  a  week,  what  time  will  it  indicate 
at  noon  on  January  31  ? 

125.  Earth,  Mars,  and  Saturn  were  in  the  same  straight 
line  on  the  same  side  of  the  sun  in  1875.  Taking  the  period 
of  revolution  of  Mars  about  the  sun  as  If  yr.,  and  that  of 
Saturn  as  29^  y  r.,  in  what  year  will  they  again  be  in  the  same 
relative  positions  and  in  the  same  direction  from  the  sun? 


MISCELLANEOUS  PROBLEMS  279 

126.  If  the  cotton  crop  of  Mississippi  decreased  5%  in  a 
certain  year,  amounting  to  1,347,100  bales,  how  many  bales 
were  produced  before  the  decrease  ? 

127.  The  world^s  production  of  copper  in  a  certain  year 
was  575,000  long  tons,  of  which  the  United  States  produced 
308,000.  Of  the  United  States,  the  largest  producers  were 
Michigan,  192  million  pounds,  and  Montana,  27%  more 
than  Michigan.  What  per  cent  of  the  world's  production 
was  that  of  the  United  States?  of  Michigan?  of  Montana? 

128.  What  is  the  present  worth  of  (or  sum  which  put  at 
interest  will  amount  to)  $230.25,  due  in  3  yr.  9  mo.  18  da., 
money  being  worth  6%  ?  If  we  call  the  difference  between 
the  present  worth  and  the  given  sum  (or  future  worth)  the 
true  discount,  as  was  formerly  the  custom,  find  the  true 
discount  in  this  case. 

129.  What  is  the  present  worth  (see  Ex.  128)  of  $151.33, 
due  in  4  mo.  15  da.,  money  being  worth  6%  ? 

130.  What  is  the  present  worth  and  true  discount  (see 
Ex.  128)  of  $161.50,  due  in  1  yr.  3  mo.  10  da.,  money  being 
worth  6%  ? 

131.  The  following  are  some  of  our  greatest  coal-pro- 
ducing states,  with  the  number  of  tons  produced  by  each  in 
a  certain  year,  and  the  value  of  the  coal  at  the  mines.  Eind 
the  value  per  ton  in  each  case. 

Alabama  11,700,000  T.  $14,375,000 

Colorado  7,652,000  T.  $9,182,400 

Illinois  34,955,000  T.  $36,353,200 

Indiana  11,191,700  T.  $12,310,870 

Kentucky  7,075,000  T.  $7,145,750 

Ohio  24,574,000  T.  $29,488,800 

Pennsylvania  103,000,000  T.  $115,360,000 

West  Virginia  26,883,000  T.  $28,227,150 


,^ 


>^ 


TABLES  FOE,  EEFEEENCE 

Length 

12  Inches  (in.)  =  1  foot  (ft.). 
3  feet  =1  yard  (yd.). 
5i^  yards,  or  16  J^  feet  =  1  rod  (rd.). 
320  rods,  or  5280  feet  =  1  mile  (mi.). 

4  inches  =  1  hand. 
6  feet  =  1  fathom. 
120  fathoms  =  1  cable  length. 
1.15  common  miles  =  1  knot  (nautical  mile). 

Square  Measure 

144  square  inches  (sq.  in.)  =  1  square  foot  (sq.  ft.). 
9  square  feet  =  1  square  yard  (sq.  yd.). 
30 J-  square  yards  =  1  square  rod  (sq.  rd). 
160  square  rods  =:  1  acre  (A.). 

640  acres  =  1  square  mile  (sq.  mi.). 

Cubic  Measure 

1728  cubic  inches  (cu.  in.)  =1  cubic  foot  (cu.  ft.). 
27  cubic  feet  =  1  cubic  yard  (cu.  yd.). 
V2S  cubic  feet  =  1  cord  (cd.). 
24|  cubic  feet  =  1  perch  (stone,  etc.). 

Weight 

16  ounces  (oz.)  =  1  pound  (lb.). 
2000  pounds  =  1  ton  (T^.). 

100  pounds  =  1  hundredweight  (cwt.). 
112  pounds  =  1  long  hundredweight. 
2240  pounds  =  1  long  ton. 

Troy  Weight 

24  grains  (gr.)  =  1  pennyweight  (pwt.  or  dwt.). 
20  pennyweights  =  1  ounce  (oz.). 
12  oz.  =  1  pound  (lb.). 
The  avoirdupois  pound  contains  7000  gr.,  the  Troy  pound  6760  gr. 

3.2  grains  =  1  carat  (diamond  weight). 
But  "  16  carats  fine  "  means  if  pure  gold. 

280 


TABLES  FOR  REFERENCE  281 


Apothecaries^  Weight 

20  grains  (gr.)  =  1  scruple  (sc.  or  B). 
3  scruples  =  1  dram  (dr.  or  5). 
8  drams  =  1  ounce  (oz.  or  § ). 
12  ounces  —  1  pound  (lb.). 


Liquid  Measure 

4  gills  (gi.):=l  pint  (pt.). 
2  pints  =  1  quart  (qt.) . 
4  quarts  =  1  gallon  (gal.). 
231  cubic  inches  =  1  gallon. 

31.5  gallons  =  1  barrel  (bbl.)  (varies). 
2  barrels  =  1  hogshead  (varies). 
16  fluid  ounces  =  1  pint  (apothecaries'). 
67.75  cubic  inches  =  1  liquid  quart. 


Dry  Measure 

2  pints  (pt.)  =  1  quart  (qt.). 
8  quarts  =  1  peck  (pk.). 
4  pecks  =  1  bushel  (bu.). 

2150.42  cubic  inches  =  1  bushel. 
67.2  cubic  inches  =  1  dry  quart. 

Time 

60  seconds  (sec.)  =  1  minute  (min.). 
60  minutes  =  1  hour  (hr.). 
24  hours  =  1  day  (da.). 
7  days  =  1  week  (wk.). 
12  months  (mo.)  =  1  year(yr.). 

Value 

10  mills  =  1  cent  (ct.  or  f)o 
10  cents  =  1  dime  (d.). 
10  dimes  =  1  dollar  {$). 
10  dollars  =  1  eagle  (E.). 


282  TABLES  FOR  REFERENCE 

Angles  and  Arcs 

60  seconds  (6O'0  =  1  minute  (1'). 
60  minutes  =  1  degree  (1°) . 
90  degrees  =  1  right  angle. 
360  degrees  =  1  circumference. 

Surveyors'  Table  of  Length 

7.92  inches  =  1  link  (li.). 
100  links  =  4  rods  =  1  chain  (ch.). 
SO  chains  =  5280  ft.  =  1  mile. 

City  property  is  usually  measured  by  feet  and  decimal  fractions  of 
a  foot ;  farm  property,  by  rods  or  chains. 


Surveyors'  Table  of  Square  Measure 

16  square  rods  (sq.  rd.)  =  1  square  chain  (sq.  ch.). 
10  square  chains  =  1  acre  (A.). 

640  acres  =  1  square  mile  (sq.  mi.). 
36  square  miles  =  1  township  (tp.). 
A  square  rod  was  formerly  called  a  petxh. 
A  quarter  of  an  acre  (40  sq.  rd.)  was  formerly  called  a  rood. 

Counting 

12  units  —  1  dozen. 
12  dozen,  or  144  =  1  gross  (gr.) . 
12  gross,  or  1728  =  1  great  gross. 
20  units  =  1  score. 


Paper 

24  sheets  =  1  quire. 
20  quires  ==  480  sheets  =  1  ream. 

Now,  for  convenience  in  counting,  600  sheets  are  more  often  called 
a  ream;  and  the  word  quire  is  used  only  for  folded  note  paper,  other 
paper  being  usually  sold  by  the  pound. 




10,000  meters. 
1000      *' 

= 

100      " 
10      " 

_ 

0.1      of  a  meter. 

= 

0.01 

it 

= 

0.001 

a 

TABLES  FOR  REFERENCE  283 

Metric  Length  _.  - ^^-J 

A  myriameter 

A  kilometer  (km.  or  Km.)  = 

A  hektometer(Hm.) 

A  dekameter(Dm.) 

Meter  (m.) 
A  decimeter  (dm.) 
A  centimeter  (cm.) 
A  millimeter  (mm.) 

1  meter  =  nearly  39.37  inches. 
1  kilometer  =  nearly  0.6  mile. 


Metric  Squai^e  Measure 

A  square  myriameter  =  100,000,000  square  meters. 

*'       kilometer  (km2.)       =      1,000,000       "  ** 

*'       hektometer  =  10,000       "  '* 

"       dekameter  =  100       ''  '' 

Square  meter  (m2.) 
A  square  decimeter  (dm2.)        =  0.01  of  a  square  meter. 

"       centimeter  (cm2.)       =  0.0001         *'  " 

**       millimeter  (mm2.)      =  0.000001     "  '» 

The  abbreviation  sq.  m.  is  often  used  for  m^.,  sq.  dm.  for  dm^.,  etc. 
A  square  dekameter  is  called  an  are  (land  measure). 

100  ares  :=  1  hektare  (about  2.47  acres). 


Metric  Cubic  Measure 

A  cubic  myriameter  =  10^2  cubic  meters. 

"•       kilometer  =  10^'*         *' 

**       hektometer  =1,000,000       *'        " 

"       dekameter  =  1000       '•'•        '' 

Cubic  meter  (m^.) 

A  cubic  decimeter  (dm^.)  =  0.001       of  a  cubic  meter. 

»*       centimeter  (cm^.)  =  0.000001         ''        *' 

**       millimeter  (mm3.)  =  0.000000001  **         ** 

A  cubic  meter  is  called  a  stere  (in  wood  measure). 


284  TABLES  FOR  REFERENCE 

Metric  Cajjacity 
A  hektoliter  (hi.  or  HI.)  =  100  liters.. 


A  dekaliter  (Dl.) 

=    10     *' 

Liter  (1.) 

A  deciliter  (dl.) 

=     0.1      of  a  liter. 

A  centiliter  (cl.) 

=     0.01 

A  milliliter  (ml.) 

=     0.001 

1  liter  =  1  cubic  decimeter  =  nearly  1  quart. 

.  liter  of  water  weighs  approximately  1  kilogram. 

Metric 

Weight 

A  metric  ton  (t.  or  M.t.) 

=  1,000,000  grams.      \ 

A  quintal  (q. ) 

=     100,000       " 

A  myriagram  (Mg.) 

=       10,000       " 

A  kilogram  (kg.  or  Kg.) 

=          1000       " 

A  hektogram  (Hg.) 

100       " 

A  dekagram  (Dg.) 

10       '' 

;                Gram  (g.) 

;        A  decigram  (dg.) 

=                0. 1      of  a  gra 

,  \      A  centigram  (eg.) 

0.01 

A  milligram  (mg.) 

0.001 

The  metric  ton  is  nearly  the  weight  of  1  m^.  of  water  at  its  greatest 
density  ;  the  kilogram,  of  1  dm^.  ;  and  the  gram,  of  1  cm^. 
A  kilogram  is  about  2i  lb.  ;  a  metric  ton  about  2205  lb. 

English  Money 

12  pence  (d.)  =1  shilling  (s.)  =  $0,243  +. 
20  shiUings  =  1  pound  (£)    =  $4.8665. 

French  Money 

100  centimes  (c.)  =  1  franc  (fr.)  =  $0,193. 
This  system  is  used  in  several  European  countries. 

German  Money 
100  pfennigs  (pf.)  =  1  mark  (M.)  =  $0,238. 


DEFINITIONS  OF  THE  MOST  COMMON  TEEMS 
USED  IN  AEITHMETIC 

Abstract  number.  A  number  that  does  not  refer  to  any  particular 
kind  of  object  or  measure  is  called  an  abstract  number.  All  numbers 
are,  however,  essentially  abstract,  whether  the  kind  of  thing  numbered 
is  mentioned  or  not. 

Addends.   Numbers  to  be  added  are  called  addends. 

Addition.  The  process  of  finding  a  number  that  equals  two  or 
more  numbers  taken  together  is  called  addition. 

Aliquot  part.  A  number  which  is  contained  in  a  given  number  an 
integral  number  of  times  is  called  an  aliquot  part  of  that  number. 
Thus  12 1  is  an  aliquot  part  of  100. 

Amount  of  note.  The  sum  of  the  principal  (or  face)  and  interest  of 
a  note  is  called  the  amount. 

Analysis.  In  arithmetic  the  process  of  reasoning  to  find  out  a 
truth  is  called  analysis. 

Antecedent.   The  first  term  of  a  ratio  is  called  the  antecedent. 

Arc.   A  portion  of  a  circumference  is  called  an  arc. 

Area.  The  number  of  square  units  contained  in  a  surface  is  called 
its  area. 

Arithmetic.  The  science  that  treats  of  numbers  and  their  applica- 
tions is  called  arithmetic. 

Assets.  The  property  of  an  individual  or  corporation  is  called  the 
assets. 

Average.  The  sum  of  n  given  numbers,  divided  by  n,  is  called 
their  average.    Thus  the  average  of  three  numbers  is  J  of  their  sum. 

Bank.  An  establishment  for  the  transaction  of  the  business  of 
loaning  sums  of  money,  receiving  money  on  deposit,  and  exchange, 
is  called  a  bank. 

Bank  discount.  The  interest  paid  in  advance  on  money  borrowed 
at  a  bank  is  called  bank  discount. 

Base.  The  number  of  which  some  per  cent  is  to  be  found  is  called 
the  base.  The  line  on  which  a  figure  appears  to  stand  is  called  the 
base. 

Bill.  A  written  statement  of  goods  sold  or  of  work  done  is  called 
a  bill. 

Bill  of  exchange.   A  foreign  draft  is  often  called  a  bill  of  exchange. 

286 


286  DEFINITIONS  OF  COMMON  TERMS 

Bond.  A  written  or  printed  promise  to  pay  a  certain  sum  at  a 
specified  time,  signed  by  the  maker  and  bearing  his  seal,  is  called  a 
bond. 

Cancellation.  Dividing  both  terms  of  a  fraction  by  the  same  fac- 
tor is  called  cancellation.    The  factor  is  then  said  to  be  canceled. 

Capacity.  The  measure  of  a  receptacle,  indicating  the  number  of 
units  it  contains,  is  called  the  capacity. 

Capital.  The  money  contributed  by  the  stockholders  to  maintain 
a  corporation  is  called  its  capital  or  capital  stock. 

Check.  An  order  on  a  bank  to  pay  money  is  called  a  check.  An 
operation  that  tends  to  verify  another  one  is  called  a  check. 

Circle.  A  figure  bounded  by  a  curve,  ev^ry  point  of  which  is  equi- 
distant from  a  point  within  called  the  center,  is  called  a  circle. 

Circumference.  The  bounding  line  of  a  circle  is  called  its  circum- 
ference.   In  advanced  mathematics  circle  is  used  for  circumference. 

Commission.  The  percentage  charged  by  an  agent  for  transacting 
business  is  called  commission. 

Common  denominator.  A  denominator  common  to  two  or  more 
fractions  is  called  a  common  denominator  of  the  fractions. 

Common  divisor.  A  factor  that  is  common  to  two  or  more  num- 
bers is  called  a  common  divisor  or  common  factor. 

Common  factor.    See  Common  Divisor. 

Common  fraction.  A  fraction  having  both  terms  fully  expressed  by 
figures  is  called  a  common  fraction. 

Common  multiple.  A  multiple  of  each  of  two  or  more  numbers  is 
called  a  common  multiple  of  the  numbers. 

Complex  fraction.  A  fraction  that  has  a  fraction  in  either  numer- 
ator or  denominator,  or  both,  is  called  a  complex  fraction. 

Composite  number.  A  number  not  prime  is  called  a  composite 
number. 

Compound  fraction.  An  expressed  multiplication  of  an  integer  or 
a  fraction  by  a  fraction  is  called  a  compound  fraction ;  for  example, 
I  of  7  or  f  of  f . 

Compound  interest.  If  interest  is  not  paid  when  due,  but  is  added 
to  the  principal  to  form  a  new  principal,  and  interest  is  reckoned  on 
this  amount,  the  obligation  is  said  to  draw  compound  interest. 

Compound  numbers.  Denominate  numbers  in  which  two  or  more 
units  are  expressed  are  called  compound  numbers. 

Concrete  number.  A  number  that  refers  to  some  particular  kind  of 
object  or  measure  is  called  a  concrete  number. 


DEFINITIONS  OF  COMMON  TERMS  287 

Consequent.   The  second  term  of  a  ratio  is  called  the  consequent. 

Consignee.  The  person,  firm,  or  corporation  to  which  goods  are 
sent  (consigned)  is  called  a  consignee. 

Consignor.  The  one  who  sends  (consigns)  goods  to  another  is  called 
a  consignor. 

Corporation.  A  number  of  individuals  organized  by  law  to  act  as 
one  body  is  called  a  corporation ;  also  called  a  company. 

Coupon.  A  note  attached  to  a  bond,  promising  to  pay  the  regular 
interest,  to  be  cut  off  and  presented  for  payment  when  due,  is  called 
a  coupon. 

Creditor.  A  person  to  whom  another  owes  money  is  called  his 
creditor. 

'  Cube.   A  regular  solid  with  six  equal  squares  as  faces  is  called  a 
cube.    The  third  power  of  a  number  is  called  its  cube. 

Cube  root.  One  of  the  three  equal  factors  of  a  number  is  called 
its  cube  root. 

Customhouse.  The  place  where  government  duties  on  imported 
goods  are  received  is  called  a  customhouse. 

Debtor.    A  person  who  owes  money  to  another  is  called  his  debtor. 

Decimal  fraction.  A  fraction  whose  denominator  is  not  written, 
but  is  10  or  some  power  of  10,  is  called  a  decimal  fraction. 

Decimal  point.  A  period  written  before  tenths  in  a  decimal  frac- 
tion is  called  a  decimal  point. 

Decimal  system.  A  system  of  numbers  based  upon  the  powers  of 
ten  is  called  a  decimal  system;  for  example,  our  common  system  of 
numbers  and  the  metric  system. 

Denominate  numbers.  Concrete  numbers  denoting  measure  (includ- 
ing weight)  are  called  denominate  numbers. 

Denominator.  The  number  which  shows  into  how  many  equal 
parts  a  unit  has  been  divided  is  called  the  denominator  of  the  fraction, 
—  in  a  common  fraction,  the  number  below  the  line. 

Difference.  The  number  which  added  to  one  number  makes  another 
is  called  the  difference  between  them.  It  is  the  result  in  taking  one 
number  from  another. 

Discount.  A  deduction  made  on  a  price  or  amount  is  called  a  dis- 
count. The  difference  between  the  face  or  par  value  and  a  less  market 
value  is  also  called  a  discount,  as  when  stocks  sell  at  10%  discount. 
Interest  paid  in  advance  on  a  note  is  called  discount. 

Dividend.  The  number  to  be  divided  is  called  the  dividend.  It  is 
the  given  product  of  the  quotient  and  divisor. 


288  DEFINITIONS  OF  COMMON  TERMS 

Dividends.  The  shares  of  the  earnings  divided  at  intervals  among 
the  stockholders  of  a  corporation  are  called  dividends,  a  stockholder 
being  said  to  receive  a  dividend. 

Division.  The  operation  by  which,  given  the  product  of  two  num- 
bers and  one  of  them,  the  other  is  found,  is  called  division. 

Divisor.  The  number  by  which  the  dividend  is  divided  is  called  the 
divisor. 

Draft.  A  check  drawn  by  one  bank  on  another,  or  by  one  indi- 
vidual on  another,  is  called  a  draft. 

Drawee.  A  person  to  whose  order  a  draft  is  payable  is  called  the 
drawee. 

Drawer.   A  person  who  signs  a  draft  is  called  the  drawer. 

Duties.  Government  taxes  on  imported  goods  are  called  duties. 
Some  governments  levy  taxes  on  exported  goods,  and  they  are  also 
called  duties. 

Equation.  The  expressed  equality  of  two  quantities  is  called  an 
equation. 

Equilateral  triangle.  A  triangle  whose  three  sides  are  equal  is 
called  an  equilateral  triangle. 

Even  number.  A  number  that  contains  the  factor  2  is  called  an 
even  number. 

Evolution.  The  process  of  finding  a  root  of  a  number  is  called 
evolution. 

Exact  interest.  Interest  reckoned  on  the  basis  of  365  days  to  the 
year  is  called  exact  interest. 

Exchange.  The  payment  of  money  by  means  of  checks,  money 
orders,  or  drafts,  is  called  exchange. 

Exponent.  A  small  figure  placed  at  the  right  and  a  little  above  a 
number  is  called  an  exponent.  If  it  is  an  integer,  it  shows  how  many 
times  the  other  number  is  taken  as  a  factor  ;  thus,  3^  =  3  x  3  =  9. 
There  are  also  fractional  exponents,  where  the  denominatojr^indicates 
a  root  and  the  numerator  a  power  ;  thus,  8^  means  ^8^  =  ^64  =  4. 

Extremes  and  means.  The  first  and  last  terms  of  a  proportion  are 
called  the  extremes;  the  second  and  third,  the  means. 

Face  of  note.  The  principal  mentioned  in  a  note  is  called  the  face 
of  the  note. 

Factors.  The  numbers  which  multiplied  together  make  another 
number  are  called  its  factors.  (This  definition  is  limited  to  integers, 
except  in  speaking  of  roots.)  In  some  lines  of  business  agents  are 
called  factors. 


DEFINITIONS  OF  COMMON  TERMS  289 

Fraction.  One  or  more  of  the  equal  parts  of  a  unit  is  called  a  frac- 
tion. In  general,  any  indicated  division  in  the  form  -  is  called  a 
fraction. 

Greatest  common  divisor.  The  greatest  factor  common  to  two  or 
more  numbers  is  called  their  grrea^es^  common  divisor.  It  is  also  called 
greatest  common  measure. 

Improper  fraction.  A  fraction  whose  numerator  equals  or  exceeds 
the  denominator  is  called  an  improper  fraction. 

Index.  A  figure  written  in  a  radical  sign  to  indicate  what  root  is 
to  be  extracted  is  called  an  index  of  the  root ;  thus,  Vs  means  the 
cube  root  of  8.    In  square  root  the  index  is  not  written,  as  Vi. 

Indorse.  To  write  one's  name  on  the  back  of  a  note  or  other 
document  is  to  indorse  it. 

Insurance.  An  agreement  to  compensate  any  one  for  some  specified 
loss  is  called  insurance. 

Integer.   See  Number. 

Integral  number.  An  integer  is  also  called  an  integral  or  whole 
number. 

Interest.    Money  paid  for  the  use  of  money  is  called  interest. 

Involution.  The  process  of  finding  a  power  of  a  number  is  called 
involution. 

Isosceles  triangle.  A  triangle  two  of  whose  sides  are  equal  is  called 
an  isosceles  triangle. 

Latitude.  The  degree  measure  of  the  distance  of  a  place  from  the 
equator  is  called  its  latitude. 

Least  common  denominator.  The  least  denominator  common  to 
several  fractions  is  called  their  least  common  denominator. 

Least  common  multiple.  The  least  of  all  the  common  multiples  of 
two  or  more  numbers  is  called  their  least  common  multiple. 

Length.  The  number  of  linear  units  a  figure  contains  is  called  its 
length. 

Liability.   An  obligation  to  pay  money  is  called  a  liability. 

Like  numbers.  Numbers  referring  to  the  same  unit  are  called  like 
numbers ;  thus,  2  ft.  and  3  ft. 

Longitude.  The  degree  measure  of  the  distance  of  a  place  from  a 
prime  (or  standard)  meridian  (usually  the  one  through  Greenwich, 
England)  is  called  its  longitude. 

Lowest  terms.  If  the  terms  of  a  fraction  are  prime  to  each  other 
the  fraction  is  said  to  be  reduced  to  its  lowest  terms. 

Maker  of  a  note.  The  one  who  signs  a  note  is  called  the  maker. 


290  DEFINITIONS  OF  COMMON  TERMS 

Maturity.  The  date  on  which  a  note  or  bond  is  due  is  called  the 
date  of  its  maturity. 

Mean  proportional.  If  the  two  means  of  a  proportion  are  equal, 
either  is  called  the  mean  proportional  between  the  extremes. 

Means.   See  Extremes. 

Minuend.   The  number  from  which  we  subtract  is  called  the  minuend. 

Mixed  decimal.  A  number  composed  of  an  integer  and  a  decimal 
fraction  is  called  a  mixed  decimal. 

Mixed  number.  The  sum  of  a  whole  number  and  a  fraction  is  called 
a  mixed  number. 

Multiple.  The  product  of  two  abstract  integers  is  called  a  multiple 
of  either. 

Multiplicand.   The  number  multiplied  is  called  the  multiplicand. 

Multiplication.  The  process  of  taking  one  number  as  many  times 
as  there  are  units  in  another  is  called  multiplication  (by  an  integer). 

Multiplier.  The  number  by  which  we  multiply  is  called  the 
multiplier. 

Mutually  prime  numbers.  Numbers  that  have  no  common  factor 
except  one  are  said  to  be  prime  to  each  other.,  or  mutually  prime. 

Net  proceeds.  The  money  that  remains  after  all  discounts  and 
charges  are  paid  is  called  the  net  proceeds  of  any  sum. 

Notation.  The  writing  of  numbers  by  means  of  symbols  is  called 
notation. 

Note.   See  Promissory  Note. 

Number.  A  unit  or  a  collection  of  units  is  called  a  whole  number 
or  an  integer.    See  also  Fraction. 

Numeration.   The  naming  of  numbers  is  called  numeration. 

Numerator.  The  number  which  shows  how  many  parts  have  been 
taken  to  make  a  fraction  is  called  the  numerator,  — in  a  common  frac- 
tion, the  number  above  the  line. 

Obligation.  A  sum  which  a  person  is  obliged  to  pay  is  called  an 
obligation. 

Odd  number.    A  number  that  is  not  even  is  called  an  odd  number. 

Order.  In  writing  numbers  the  place  occupied  by  a  figure  is  called 
its  order.  Thus  we  speak  of  units  of  the  second  order,  meaning  the 
tens. 

Par  value.  The  face  or  nominal  value  of  stock  is  called  its  par 
value.    In  railroad  stocks  this  is  usually  |100  a  share. 

Partial  payment.  A  part  payment  on  a  note  is  also  called  a  partial 
payment. 


DEFINITIONS  OF  COMMON  TERMS  291 

Payee.  The  person  to  whom  the  sum  mentioned  in  a  note,  check, 
draft,  or  other  similar  document  is  payable  is  called  the  payee. 

Per  cent.  Another  name  for  hundredths  is  per  cent.  It  originally 
meant  "by  the  hundred." 

Percentage.  The  result  found  by  taking  a  certain  per  cent  of  the 
base  is  called  the  percentage.  That  part  of  arithmetic  that  deals  with 
per  cent  is  often  called  percentage. 

Perimeter.  The  length  of  the  boundary  of  a  pl^.ne  figure  is  called 
the  perimeter. 

Periods.  Groups  of  three  figures  each,  marked  o^  by  a  separatrix, 
are  called  periods. 

Perpendicular.  A  line  that  makes  a  right  angle  with  another  is 
said  to  be  perpendicular  to  it. 

Place  value.  The  value  of  a  period  or  of  a  figure,  depending  upon 
its  position,  is  called  its  place  value. 

Policy.   A  written  contract  of  insurance  is  called  sl  policy. 

Poll  tax.  A  tax  on  a  person  (usually  limited  to  male  citizens  over 
twenty-one  years  of  age),  without  regard  to  the  amount  of  property 
owned,  is  called  ?i poll  tax.    (The  old  name  for  head  was  "poll.") 

Power.   The  product  of  two  or  more  equal  factors  is  called  a  power. 

Premium.  Money  paid  for  insurance  for  a  certain  time  is  called  a 
premium.  The  excess  of  the  market  value  above  the  par  value  of  stock 
or  other  evidences  of  value  is  called  a  premium. 

Present  worth.  The  present  value  of  a  debt  due  in  the  future  is 
called  the  present  worth. 

Prime  factors.  Factors  that  are  prime  numbers  are  called  prime 
factors. 

Prime  number.  A  number  that  has  no  factors  except  itself  and  one 
is  called  a  prime  number. 

Principal.  A  sum  of  •  money  that  draws  interest  is  called  the 
principal. 

Proceeds.  The  face  (or  amount,  if  it  draws  interest)  of  a  note  less 
the  discount  is  called  the  proceeds. 

Product.  The  result  of  multiplying  two  or  more  numbers  together 
is  called  the  product. 

Promissory  note.  A  paper  signed  by  a  debtor,  agreeing  to  pay 
money,  is  called  a  promissory  note. 

Proper  fraction.  A  fraction  whose  numerator  is  less  than  the 
denominator  is  called  a  proper  fraction. 


292  DEFINITIONS  OF  COMMON  TERMS 

Proportion.  An  expression  of  equality  of  two  ratios  is  called  a 
proportion. 

Quotient.   The  number  found  by  division  is  called  the  quotient. 

Rate.  The  number  of  hundredths  of  the  base  to  be  taken  is  called 
the  rate;  thus  the  rate  of  interest  may  be  6%,  the  rate  per  cent  of 
interest  being  then  6.  The  amount  of  tax  on  a  dollar  is  often  called 
the  rate  of  taxation.  The  premium  on  each  $100  of  fire  insurance  or 
each  11000  of  life  insurance  is  often  called  the  rate  of  insurance. 

Ratio.  The  relation  of  one  quantity  to  another  of  the  same  kind, 
as  expressed  by  division  of  the  first  by  the  second,  is  called  their  ratio. 

Reciprocal.  The  reciprocal  of  a  fraction  is  the  fraction  with  its 
terms  interchanged.  Unity  divided  by  any  number  is  called  the  recip- 
rocal of  the  latter. 

Reduction.  Changing  the  form  of  a  number  without  changing  the 
value  is  called  reducing  the  number.  (This  process  is  used  in  dealing 
with  fractions  and  compound  numbers.) 

Reduction  ascending.  Reduction  of  compound  numbers  to  a  higher 
denomination  is  called  reduction  ascending. 

Reduction  descending.  Reduction  of  compound  numbers  to  a  lower 
denomination  is  called  reduction  descending. 

Remainder.  The  part  of  the  dividend  remaining  when  the  division 
is  not  exact  is  called  the  remainder.  The  difference  in  subtraction  is 
also  called  the  remainder. 

Root.  One  of  the  equal  factors  of  a  number  is  called  a  root.  See 
also  Square  Root. 

Scalene  triangle.  A  triangle  whose  three  sides  are  unequal  is 
called  a  scalene  triangle. 

Separatrix.  The  comma  used  in  separating  periods  in  large  num- 
bers is  called  a  sepjaratrix. 

Share.  One  of  a  specified  number  of  equal  parts  of  the  capital 
stock  of  a  company  is  called  a  share. 

Similar  fractions.  If  several  fractions  have  the  same  denominator, 
they  are  said  to  be  similar  fractions. 

Simple  fraction.  A  common  fraction  whose  terms  are  integral  is 
called  a  simple  fraction. 

Solid.  A  magnitude  that  has  length,  breadth,  and  thickness  is 
called  a  solid. 

Square.  A  plane  figure  with  four  equal  sides  and  four  equal 
angles  is  called  a  square. 


DEFINITIONS  OF  COMMON  TERMS  293 

Square  root.  One  of  the  two  equal  factors  of  a  number  is  called 
its  square  root. 

Stockholder.  One  who  has  stock  in  a  corporation  or  company  is 
called  a  stockholder. 

Stocks.    The  shares  of  corporations  generally  are  called  stocks. 

Subtraction.  The  operation  of  finding  the  difference  between  two 
numbers  is  called  subtraction. 

Subtrahend.  The  number  which  is  subtracted  is  called  the  sub- 
trahend. 

Sum.   The  result  in  addition  is  called  the  sum. 

Surface.  A  magnitude  that  has  length  and  breadth,  but  not  thick- 
ness, is  called  a  surface. 

Tax.  Money  assessed  by  a  government  for  its  support  is  called  a 
tax. 

Terms  of  a  fraction.  The  numerator  and  denominator  together 
are  called  the  terms  of  the  fraction. 

Triangle.  A  plane  figure  formed  by  three  straight  lines  is  called  a 
triangle. 

Unit.  Any  one  thing  is  called  a  unit.  The  number  one  is  called 
unity. 

Unit  fraction.  A  common  fraction  whose  numerator  is  1  is  called 
a  unit  fraction. 

Volume.  The  number  of  cubic  units  a  solid  contains  is  called  its 
volume. 

Whole  number.   See  Number. 


INDEX 


PAGE 

Accounts 141,  162 

Addition 8,  28 

Angle  measure 49 

Antecedent 118 

Arabic  figures 1 

Army 193 

Assessed  valuation       .     .     .198 
Assessors 198 

Bank .  141 

accounts 141 

discount 150 

of  deposit 145 

savings 141 

Barometer 228 

Bill  of  goods       .     .     .     160,  167 
of  exchange      .     .     .     .176 

Birds 129 

Bonds .216 

Borrowing  money   ....  149 

Broker 212 

Brokerage 212 

Business,  entering       .     .     .  138 

Cancellation       .     .     .     .     .  101 
Capacity   .       47-49,  67,  182,  185 

Capital 210 

Cattle 97 

Checks 147,  167 

Circle,  circumference       .     .  248 

area 250 

294 


PAGE 

Circumference 248 

Clearing  house 172 

Coffee 220 

Collector  of  taxes  ....  200 
Commission  ....  200,  212 
Compound  interest      .     .     .  143 

proportion 124 

Cone     . 258 

Consequent 118 

Corporation 210 

Cotton 220 

Creamery       .     .     .     .     .     .  136 

Credit 162 

Cube  numbers  and  roots,  232,  242 
Cubic  measure   .     .    47,  182,  185 

Customhouse 195 

Cylinder 254 

Dairy  problems       .     .     .     .136 

Days  of  grace 149 

Debit 162 

Decimals.    See  the  operations. 
Decimal  system       ....       1 

Definitions 285 

Deposit,  bank  of     ...     .  145 

Directors        210 

Discount,  bank       .     .     .     .150 

trade 158 

in  exchange  ....  172 
Discounting  notes  .  .  .  .152 
Dividends      ....     210,  216 


INDEX 


295 


PAGE 

Division 20,  42 

Drafts        210,  216 

Drawee 170 

Drawer 170 

Dressmaking  problems     .     .     91 

Dry  measure 49 

Duty 195,  197 

English  money 174 

European  money     .     .     174,  187 

travel 187 

Exact  interest 108 

Excavations 70 

Excliange 167 

Extremes 122 

Face 201 

Factory  problems  .  .  .  .114 
Farm  problems  .  .  60,  128,  136 
Fertilizers  .  .  .  .  131,  132 
Foreign  exchange   .     .     .     .174 

money 174 

Fractions.    See  the  operations. 
French  money 174 

German  money  .  .  .  .174 
Government  expenses      .     .190 

Grain 219 

Grocery  problems   .     .       92,  115 

Hindoo  figures 1 

Hypotenuse 238 

Indorser    .     .     .       147,  149,  168 
Industrial   problems,   60,    91, 
92,97,98,114,115,128, 

221,  224,  225,  227 
Insurance 201 


PAGE 

Interest,  compound     .     .     .  143 

exact 108 

simple 99 

tables 107 

Iron  working 225 

Lard,  dealings  in    ...     .  220 

Laws  of  operations      ...  27 

Length      ....     47,  53,  179 

Life  insurance    .....  206 

Liquid  measure       .     .     .     .  48 

Local  taxes 198 

Longitude  and  time     ...  75 

Marine  insurance    ....  205 

Means 122 

Measures 47,  67 

Mensuration 248 

Merchants'  rule       .     .     .     .157 

Meridian 65,  75 

Meteorology       228 

Metric  system     .     .     .     178,  187 
Mixed  numbers.    See  the 
operations. 

Model  order 160 

bill 160 

Money  order 167 

Mortgage        216 

Multiplication     .     .     .     .   15,  35 

Navy 193 

Note 149 

Numerals 1 

Ocean  traffic 277 

Operations     ......  27 

See  Addition,  etc. 

Ordering  goods  .     .     .     .     .  160 

Oyster  industry 98 


296 


INDEX 


1*AGE 

Par  of  exchange      ....  172 

of  stock        212 

Parallelogram  .....  61 
Partial  payments  ....  154 
Partitive  proportion    .     119,  164 

Partnership 164 

Payee  .     .     .     .     .     .     147,  170 

Percentage 84 

It 248 

Policy 201,  207 

Poll  tax 198 

Pork 219 

Post  office 192 

Postal  money  order     .     .     .   167 

Powers 230,  232 

Premium  on  exchange      .     .172 

on  policy 201 

Price  lists 159 

Prism 252 

Proceeds 150,  170 

Produce 219 

Promissory  note  .  .  .  .149 
Proportion     .     .     .     .     117,  121 

Public  lands        65 

Pyramid 257,  259 

Rate  of  dividend  ....  210 
of  exchange  .  .  .  .172 
of  taxation       .     .     .     .198 

Ratio 117 

Roman  figures  .....  1 
Roots 230 

Savings  bank 141 

Scales 3 

Shares  of  stock 210 

Short  methods 28 

Simple  interest 99 

proportion  .     .117,  121,  124 


PAGE 

Six  per  cent  method    .     .     .  102 

Slant  height 259 

Specific  gravity       .     .     .     .184 

Sphere 261 

Square  measure       .     .       47,  181 

numbers 230 

root 230,  234 

Standard  time 80 

State  taxes 198 

Stock 210 

Subtraction 12,  32 

Sugar  industry 224 

Surveyors'  tables    .     .     .53,  54 

Table  of  time      ...       49,  105 
Tables       .     .      49,  178,  200,  280 

Tariff 195 

Tax  table 200 

Taxes 190 

Temperature 228 

Time 49,  75,  105 

Townships 65 

Trade  discount 158 

Transportation  problems      .  227 

Trapezoid 63 

Travel,  problems  of     .     .     .  187 
Triangles        62 

Uniform  scale 3 

United  States  rule        .     .     .   154 
« Units 5 

Value 49 

Varying  scale 3 

Volume      .     .  47,  48,  49,  67,  252 

Weather 228 

Weight 48,  183 

Zero 1 


ANSWERS 


Page  2 

1.  1669,  1344.      2.  XLIX,  LXXIX,  XCIV,  XCVI,  XCIX,  CXLVI. 

4.  21,000,475.  5.   1,001,001,001.0001. 

6.   1,000,958,326.0001,  1,001,000,988.7551,  1,000,705,999.8731. 

Page  4 

3.  Ill,  222,  333,  to  999. 

4.  111,111,111,  222,222,222,  to  999,999,999. 
6.   142,857,  714,285,  571,428,  to  428,571. 

6.  111,111,  222,222,  to  999,999. 

7.  81,  9801,  998,001,  99,980,001,  9,999,800,001. 

8.  121,  12,321,  1,234,321,  12,345,654,321. 

9.  1001,  11,011,  135,135,  234,234,  345,345,  789,789. 
10.  1,  11,  111,  1111,  11,111.     8,  88,  888,  8888,  88,888. 

Page  5 

1.  Ill,  233  ft.,  0.233.. 

2.  450  in.,  192  qt.,  7360  rd.,  144  ft.,  1200  oz.,  12,0001b.,  11,664  sq.  in. 

3.  3iVft.,  14  yd.,  21  lb.,  3  mi.,  2T.,  25  gal.,  144  ft. 

4.  1782  in.,  252  in.,  380,160  in.,  48  in.,  108  in.,  84  in.,  42  in.,  270  in., 

1287  in.,  158,400  in. 

Page  7 

1.  288  doz.,  24  gross,  2  great  gross. 

2.  204  in.,  258  in.,  108  in.,  792  in. 

3.  3  ft.,  12  ft.,  144  ft.,  162  ft.,  9.9  ft. 

4.  5000  lb.,  6500  lb.,  9  lb.,  7520  lb.,  427  lb.,  99  lb. 

5.  212  qt.,  832  qt.,  71  qt.,  49  qt.,  1008  qt.,  126  qt.,  303  qt.,  560  qt. 

6.  900,  1080,  184,  10,368,  189,  2,  3960. 
27.5  1 


2  ANSWERS 

Pages  9-11 

1.3586.  3.  32  mi.  40  yd.  5.  1^?^. 

2.  358  ft.  6  in.  4.  359  bu.  2  pk.  6.  2i,  2.125  =  21. 

7.   1^2  _  24- 3  6-2.    8.  3j-i^.  Common  fractions.  9.  3.175.  Decimals. 

10.  31x  +  23?/,  3123,  32  ft.  11  in.,  32  lb.  7  oz. 

11.  $250.56.  15.  $1244.53.         19.  $2421.38.        23.  $8858.80. 

12.  $317.66.  16.  $1245.30.         20.  $3703.20.  24.  $14,585.48. 

13.  $338.45.  17.  $1831.  21.  $2601.  25.  $23,135.89. 

14.  $443.10.  18.  $793.50.  22.  $3314.63.        26.  $18,237.87. 

27.  80,467,  $2,769,197,978,  1,415,539,  $565,1Q3,062,  $2,646,580,941, 

$3,968,616,096. 

28.  Columns:  407,600,000,  $4,469,100,000,  $1,593,400,000, 

^881,800,000. 
Rows:  $2,272,400,000,  $1,457,800,000,  $761,000,000, 
$1,123,700,000,  $817,800,000,  $376,900,000,  $134,700,000. 


Pages  13,  14 

1.  $154.55.  15.  88  T.  1987  lb.              29.  8  yr.  5  mo.  18  da. 

2.  $83.56.  16.  $3078.                           30.  10  yr.  9  mo.  19  da. 

3.  $200.43.  17.  30  mi.  5258  ft. 

4.  $297.04.  18.  30  T.  1978  1b. 

5.  $103.59.  19.  $1,092,855,499. 

6.  $331.85.  20.  $10,219,191,055. 

7.  $681.35.  21.  $1,142,901,501.75. 

8.  $228.95.  22.  219. 

9.  $308.25.  23.  2.19. 

10.  $1806.55.  24.  21  ft.  11  in. 

11.  $1664.50.  25.  21  lb.  15  oz. 

12.  $3987.20.  26.  2  ft. 

13.  $88.87.  .      27.   1999  1b. 

14.  88  mi.  5267  ft.       28.   11  mo. 
44.  78  cu.  ft.  1421|i  cu.  in.         45.  195  da. 

46.  103  da.  6  hr.  2  min.  33}  sec. 

47.  $147,546,695,  $153,082,710,  $185,027,555,  $124,973,766, 

$610,630,726. 

48.  966,779,  2,447,344,  3,111,349,  4,162,229. 

49.  1,480,565,  2,144,570,  3,195,450. 

50.  664,005,  1,714,885. 


33. 

1438f 

34. 

6924if. 

35. 

2303^5-. 

36. 

1244;^. 

37. 

4304^-^^. 

38. 

6597f}. 

39. 

12  ft.  7J  in. 

40. 

102  lb.  lOf  oz. 

41. 

228  gal.  2jV  qt- 

42. 

1894^V- 

43. 

58  sq.  ft. 

54 1  sq.  in. 

23  hr. 

1  min.  53.25  sec. 

ANSWERS 


Page  16 

1.  1225,  121  ft.  11  in.,  7  mi.  625  ft. 

2.  15,799,  1570  lb.  3  oz.,  151  mi.  39  rd. 

3.  12,168,  $121.68,  1215  ft.  6  in.,  117,468. 

4.  10,700,  104  sq.  ft.  124  sq.  in.,  100,700. 

5.  $83,806.25,  83,578  mi.  165  rd.,  83,508,125. 

6.  $1132.80,  1150  gal.  2  qt.,  1160  yd.  1  ft. 

7.  $2,551,900.50,  255,042  da.  7  hr.  30  min. 

8.  1,080,000,  10,746  sq.  ft.  76  sq.  in.,  10,642,500. 


9. 

351,155. 

'     18.  $179,762.50. 

27 

.  1562  ft.  4  in. 

10. 

1,183,896. 

19.  $158,397.76. 

28 

.  5615  ft.  8  in. 

11. 

1,244,078. 

20.  $274,533 

29 

.  25  1b. 

12. 

1,394,196. 

21.  $224,820.80. 

30 

.  3801b.  15  oz. 

13. 

4,700,094. 

22.  $248,718.25. 

31 

.  4841b.  5  oz. 

14. 

2,672,768. 

23.  $409,149.78. 

32 

.  558  1b. 

15. 

2,713,634. 

24.  $706,362.93. 

33 

.  1188  ft. 

16. 

5,921,013. 

25.  470  ft.  4 

in. 

17. 

$56,962.75 

26.  952  ft. 

Pages  18,  19 

1. 

486. 

22. 

20.9934. 

41. 

10873.5. 

60. 

905  lb.  7i  oz. 

2. 

247. 

23. 

5601.76. 

42. 

23636.8. 

61. 

1610  yd.  21  in. 

3. 

696. 

24. 

1064.45. 

43. 

222.3056. 

62. 

17266|i. 

4. 

36f. 

25. 

4.784. 

44. 

2.118924. 

63. 

49,063/^. 

5. 

llj. 

26. 

8.27891. 

45. 

4.017263. 

64. 

531,701/^. 

6. 

15|. 

27. 

15.50625. 

46. 

58037.58. 

65. 

49,36611. 

7. 

^' 

28. 

4.59375. 

47. 

tV- 

66. 

109,222|. 

8. 

30^. 

29. 

5.72832. 

48. 

tV 

67. 

32,781^-2^. 

9. 

33^. 

30. 

123.6552. 

49. 

I 

68. 

$23.01. 

12. 

105.3. 

31. 

189.3758. 

50. 

1- 

69. 

$47.84. 

13. 

147.84. 

32. 

355.1936. 

51. 

h 

70. 

$95.90. 

14. 

246.33. 

33. 

3.67536. 

52. 

m- 

71. 

$42.19. 

15. 

810.46. 

34. 

5.18616. 

53. 

$4424.76. 

72. 

$225.47. 

16. 

788.42. 

35. 

1015.6708. 

54. 

$5266.93. 

73. 

1211  ft.  9  in. 

17. 

0.9625. 

36. 

$35,062. 

55. 

$5645.75. 

74. 

69  T.  600  lb. 

18. 

9.35. 

37. 

$53,865. 

56. 

$12,952.1^ 

k 

76. 

115A  in. 

19. 

65.4481. 

38. 

$43.2717. 

57. 

$53,609.20. 

76. 

406f. 

20. 

5.214. 

39. 

$591.2136. 

58. 

$82,084.86. 

21. 

1.17304. 

40. 

4823. 

59. 

335  ft.  10  in. 

ANSWERS 


Pages  22,  23 

1.  281.  16.  6Sj\.  28.  70|Jf.  40.  91. 

2.  23.  17.  33.  29.  24818/3..  41.  23. 

3.  23.  18.  1891.  30.  92.  42.  32. 

4.  138 yd.,. $0. 26 1.   19.  11.  31.  22.  43.  44. 

8.  42.  "    20.  43.  32.  99.  44.  52. 

9.  37.  21.  209.  33.  84.  45.  3.25  1b. 

10.  49.  22.  313.  34.  221.  46.  $129. 

11.  62.  23.  21.  35.  13.  47.  $146.25. 

12.  1141.  24.  211^f.  36.  23.  48.  0.75  A. 

13.  37.  '  25.  309.  37.  41.  49.  13. 

14.  146.  26.  129.  38.  63.  50.  4. 

15.  42.  27.  32.  39.  91. 


Page  24 


1. 

81  gal.  3  qt. 

6. 

12. 

11. 

30ifff 

2. 

39  yd.  4/1  in. 

7. 

23  hr.  42  min.  15  sec. 

12. 

1  hr.  26  min.  39  sec. 

3. 

9. 

8. 

211cu.ft.ll792\cu.in. 

13. 

2  yd.  2  ft.  11  in. 

4. 

8. 

9. 

4. 

14. 

62  lb.  8  oz. 

5. 

12. 

10. 

14  lb.  9  oz. 

15. 

42  min.  37  sec. 

Page  25 


1. 

H- 

5. 

1- 

9. 

31. 

13.  1. 

17. 

M- 

21-  HI!- 

2. 

4i. 

6. 

tV%. 

10. 

hh- 

U.  i. 

18. 

hSh\- 

22.  t¥,v 

3. 

if 

7. 

39 
5  ■5- 

11. 

H- 

15.  3f. 

19. 

ItIIj- 

23.  6. 

4. 

u. 

8. 

H- 

12. 

li- 

16. 6. 

20. 

6. 

24.  2A. 

pase  26 

1. 

6A- 

7. 

6ii- 

13. 

3f 

19.  2||f. 

25. 

24j\. 

31.  6. 

2. 

8f|. 

8. 

4ff 

14. 

m- 

20.  lOif^. 

26. 

t'A- 

32.  8,Vt. 

3. 

lOif. 

9. 

3||. 

15. 

Sill- 

21.  llji 

27. 

4AV 

33.  3. 

4. 

nh 

10. 

4A- 

16. 

43V- 

22.  11^4. 

28. 

2. 

34.  7. 

5. 

6f. 

11. 

2t%- 

17. 

ni- 

23.  If.  ' 

29. 

3jV 

35.  7. 

6. 

5|i. 

12. 

6iJ. 

18. 

45. 

24.  5,V 

30. 

17. 

36.  4|fyd. 

ANSWERS 


Pages  30,  31 

1.  $392.20.        6.  $2772.96.      11.  $20,735.76.  16.  $934.81. 

2.  $1028.92.      7.  $2122.51.       12.  $19,521.82.  17.  6,218,295. 

3.  $1291.59.      8.  $2880.56.       13.  255  ft.  18.  9,799,016. 

4.  $2286.32.      9.  $30,328.04.   14.  771b.  5  oz.  19.  21,264,047. 

5.  $2649.64.    10.  $30,670.29.   16.   17  yr.  5  mo.  6  da.  20.  $52,962,410. 


Pages  33,  34 

1. 

$93.64. 

15. 

$12.40. 

29. 

3  yr.  277  da. 

2. 

$61.89. 

16. 

$196.42. 

30. 

4°  41'  39'', 

3. 

$109.31. 

17. 

$279.89. 

31. 

6  mi.  4755  ft. 

4. 

$330.28. 

18. 

$178.87. 

32. 

64  ft.  6  in. 

5. 

$100.09. 

19. 

$188.33. 

33. 

12°  47'  33". 

6. 

$278.78. 

20. 

$278.40. 

34. 

47  gal.  2  qt. 

7. 

$121.49. 

21. 

$123.60. 

35. 

2  yr.  3  mo. 

8. 

$239.83. 

22. 

$737.98. 

36. 

45°  40'  49". 

9. 

$732.84. 

23. 

$857.04. 

37. 

$64.21. 

10. 

$106.26. 

24. 

$1993.79. 

38. 

$237.12. 

11. 

$572.93. 

25. 

7  ft.  11  in. 

39. 

$161.41. 

12. 

$573.99. 

26. 

11  lb.  12  oz. 

40. 

277,896,484  bu 

13. 

$386.49. 

27. 

11  yd.  29  in. 

41. 

426,408,355  A. 

14. 

$588.89. 

28. 

2  mo.  23  da. 

42. 

201,926. 

43. 

$7,399,509,782. 

45. 

$7,422,907. 

44. 

1,098,861,  2,837,488,  3,975,171.         46. 

635.83 

mi.,  927.14  mi. 

Page  37 

1.  604,000,  659,375,  861,500,  $6,170,625. 

2.  33,700,  240,900,  103,400,  $1,446,400. 

3.  $856,  $409,  $5.31,  $4410.50. 

4.  100,  $5.57,  $2381.11,  $5388.56. 

5.  $27.40,  $22.44,  $9522.08,  $45,594.14. 

6.  1,  $24.86,  $316.90,  $24.72. 

7.  2961,  6714,  $8829,  5652  ft.,  13,284,  $211,329. 

8.  67,353,  41,382,  $53,207,  43,692  ft.,  $344,157. 


6  ANSWERS 

Page  43 

4.  97.26.         7.  176.22.       10.  738.96.       13.  206.67.       16.  39.488. 

5.  109.2.         8.  289.86.       11.  591.68.       14.   148.77.       17.  539.2. 

6.  139.14.       9.  548.04.      12.  654.96.       15.  266.76.       18.  319.104. 

19.  537.12,  11505.68,  $5424.84,  |17,107.72. 

20.  137.6,  $546.40,  $2211.20,  $2540. 

21.  2091.6,  $988.80,  $1462.50,  $8289.60. 

22.  149  yd.  23.  294  yd.  24.  149,707.88. 

Page  46 

1.  $36.55.  11.  If.  21.  13831.  31.  259.2. 

2.  If.  12.  79  yd.  22.  $9.05.  32.  21.44. 

3.  187ift.  13.  $41.40.  23.  if.  33.  7008  yctr-) 

4.  $15.30.  14.  1t\.  24.  46J  ft.  34.  142  gross. 
6.  I3V  15.  85imi.  25.  825.  35.  549. 

6.  59ift.  16.  $13.46.  26.  804.  36.  36  gross. 

7.  $20.55.  17.  lif.  27.  2478.  37.  72. 

8.  4^1.  18.  175|yd.  28.  11,860.  38.  48  mi. 

9.  222f  lb.  19.  2141.  29.  8175.  39.  10  mi. 
10.  $23.80.  20.  20581  30.  100.8. 

Page  52 

1.  1521  ft.,  18,252  in.   5.  3if  cu.  yd.,  164,160  cu.  in. 

2.  98  ft.,  1176  in.      6.  820|  sq.  yd.,  7386J  sq.  ft. 

3.  3  A.  80  sq.  rd.      7.  79  sq.  ft.,  11,376  sq.  in. 

4.  3106  sq.  in.  8.  35f  cu.  yd.,  960  cu.  ft.,  1,658,880  cu.  in. 
9.  4.8675  T.,  9735  lb.,  155,760  oz. 

10.  19.713  T.,  19  T.  1426  lb.,  630,816  oz. 

11.  6.875  gal.,  27.5  qt.,  55  pt. 

Page  53 

1.  80  ch.,  320  rd.,  8000  li.  7.  141611.,  14.16ch.  13.  5  ch.  28  li. 

2.  1  mi.  62  ch.,  568  rd.  8.  63,360  in.  14.  8 mi.  98 rd. 

3.  4J  ch.,  425  li.,  3366  in.  9.  14  ch.  1  rd.  15.  121  ch.  2  rd. 

4.  39.6  ft.,  660  ft.,  82.5  ft.  10.  58  ch.  71  li.  16.  476  ch.  48  li. 
6.  17.4mi.,1392ch.,5568rd.  11.  18  mi.  147  rd.  17.  318mi.64rd. 
6.  7  ch.  61  li.,  24  ch.  41  li.  12.  8  ch.  2  rd. 


ANSWERS 


Pages  55,  56 

1.  22.4  A.  6.  0.0625  A.  11.  2.026  A.  16.  20.2170  A. 

2.  18.4  A.  7.  9.01  A.  12.  10.104  A.        17.  90.0625  A. 

3.  66.7  A.  8.  5.832  A.  13.   1.7625  A.        18.  86.6472  A. 

4.  108.8  A.  9.  8.84  A.  14.  8.632  A.  19.   146.77841  A. 

5.  6.05  A.  10.  1.813  A.  15.   19.60875  A.    20.  18.63555  A. 
21.  4840  sq.  yd.,  43,560  sq.  ft.  22.  272 J  sq.  ft.,  39,204  sq.  in. 

23.  102,400  sq.  rd.,  3,097,600  sq.  yd.,  27,878,400  sq.  ft. 

24.  3.05  sq.  mi.,  1952  A.  26.  3421.68  sq.  ft. 

25.  7.8  A.,  78  sq.  ch.,  1248  sq.  rd.     27.  380  sq.  rd. 

28.  X  =  15  ch.,  2/  =  8  ch.,  100  ch.,  48  A. 

29.  22,440  sq.ft.  30.  $3825.  31.  The  second,  |140. 

32.  X  =  60  ch.,  2/  =  15  ch.,  190  ch.,  140  A. 

33.  No,  400  sq.  ch.,  300  sq.  ch.  35.  ^23,383.50. 

34.  $5400.  36.  19618.75. 


Pages  58,  59 

1. 

20  sq.  ft. 

6.  41  ch. 

11.  $13,612.50. 

2. 

7.63-V  ch. 

7.  18.6875  sq.  in. 

12.  16  ft.  4  in. 

3. 

68  ch. 

8.  16.8  ft. 

13.  32  ft.  6  in. 

4. 

121  ft. 

9.  16  ft.  6  in. 

14.  301  in. 

5. 

71ft. 

10.  32  ft. 

15.  91^11  sq.ft. 

16. 

13  yd.  8 

in. 

17.  36|sq.  yd. 

18. 

117  rd.. 

8307  sq. 

,  rd. 

,  95  rd.,  8835sq.rd. 

19. 

118f  rd., 

,  95  rd.. 

317 

Jrd.,  290  rd. 

20. 

98  ft. 

Page  60 

1.  102.24  A.,  204.52  A.,  109.2  A.,  415.96  A. 

2.  120,174.06.  6.  $571.20. 

3.  1.596  A.,  414.364  A.  7.  363  ft.,  966  ft. 

4.  $1105.  8.  42,060  sq.  ft.' 

5.  $371.70.  9.  200sq.  rd. 

Page  61 

1.  121.68  sq.  ft.     2.  39f  sq.  ft.     3.   16^  sq.  ft.     4.  7  yd.     6.  32  in. 

6.  1181.5  sq.  ft.,  26.13  sq.  in.,  43,974.4925  sq.  ft. 


ANSWERS 


Page  62 


1.  688  sq.ft.  4.  791.66^  sq.  ft.  8.  640  sq.  in. 

2.  22.785  sq.  ft.  5.  27.405  sq.  in.  9.  600  sq.  rd.,  3|  A. 

3.  34.361  sq.  in.  6.  1  sq.  yd.  108  sq.  in.  10.  25  rd.,  20  in. 

7.  7614  sq.  in. 


Page  64 

1.  38J|sq.  rd.  7.  17i  sq.  yd.  13.  1623.75  sq.  ft. 

2.  154,721  sq.  ft.  8.  3  ft.  2  in.  14.  1082.5  sq.  ft. 

3.  17,5891  sq.  ft.  9.  4056.25  sq.  ft.  15.  2706.25  sq.  ft. 

4.  52,274  sq.  in.  10.  6084.375  sq.  ft.  16.  4330  sq.  ft. 

6.  10311  sq.ft.  11.  9731.25  sq.  ft.  17.  2706.25  sq.  ft. 

6.  42641  sq.  ft.  12.  4461.875  sq.  ft.  18.  2165  sq.  ft. 


Page  66 

1.  160  A.  5.  80  A.  9.  40  A.  13.  320  A. 

2.  160  A.  6.  80  A.  10.  $10,400.  14.  480  rd. 

3.  80  A.  7.  40  A.  11.^3000.  15.  2  mi. 

4.  80  A.  8.  40  A.  12.   160  A.  16.  3  A.,  $14.25. 


Pages  68,  69 

1.  8|  cd.,  24  cd.  5.  129,600  cu.  ft. 

2.  112  loads.  6.  ^llli 

3.  .|331,  $41f.  7.  1904  cu.  ft.,  65,280  lb. 

4.  7486Jcu.ft.  8.  6000  cu.  ft. 

9.  60  cu.  ft.,  65  cu.  ft.,  103,680  cu.  in.,  112,320  cu.  in. 

10.  541  bu.  12.  4571  cu.  ft.  16.  7iT.,5|T. 

11.  7,3.  13.   16|iT.  16.  300  cu.  ft.,  8. 

14.   12  1MT. 


Page  70 

1.  13,858  cu.  yd.  4.  710f,  78|f,  21,320  ft.    7.  6,880,346^^. 

2.  19|cu.  yd.,  234cu.  yd.    5.  5.19675  da.  8.^3,^3.50. 

3.  9|lir.,  39min.  6.  $2.67. 


aStswers 


Pages  73,  74 


1. 

112,000  ( 

DU.  ft. 

9. 

7.2  in. 

17. 

$3280.50. 

2. 

6  ft. 

10. 

11  ft. 

18. 

1615f4  g{ 

3. 

16  in. 

11. 

12  ft. 

19. 

$26.58. 

4. 

112.5  sq. 

ft. 

12. 

9.5  ft.  X  12  ft.  X 12  ft. 

20. 

nn  T. 

5. 

431  ft. 

13. 

130. 

21. 

59f  f  gal. 

6. 

121  ft. 

14. 

9  ft.  X  14.3  ft.  X  16.4  ft. 

22. 

$691.20. 

7. 

27.5  ft. 

15. 

6S^\%  bu. 

\   ^ 

$46.91. 

8. 

3.9  in. 

16. 

160. 

24. 

$291.55. 

1.  First,  2  to  right,  4  up. 

2.  First,  2  to  left,  4  up. 


Page  75 


3.  First,  2  to  left,  3  down. 

4.  First,  3  to  right,  2  down. 


Page  77 

1.  1  hr.  48  min.  17  sec.  2.  5  hr.  2  min.  2  sec. 

3.   11  hr.  8  min.  10  sec.  a.m.         4.   105°,  9  p.m.        5.  4  a.m.,  8  p.m. 

6.  8  hr.  22  min.  42  sec.  a.m.,  8  hr.  2  min.  42  sec.  a.m. 


Pages  78,  79 


1. 

30°  47'  30". 

4. 

22°  45'  W. 

2. 

105°  W. 

6. 

135°  E. 

3. 
10. 

2°  5' 40.5". 
7 :  30  A.M. 

6. 

150°  E. 

11. 

46°  53'  45"  W. 

7.  37°30'W. 

8.  Fast,  3  hr.  30  min.  3  sec. 

9.  12  hr.  9  min.  38^2^  sec.  p.m. 

12.  110°  11' 12.2"  W. 

13.  17°  26' 15"  E. 


Page  82 


1.  6  hr.  9  min.  21  sec.  p.m. 

2.  9  P.M.,  6  a.m.,  4  a.m. 

3.  4  hr.  20  min.  54  sec. 

4.  9  min.  33^  sec. 
9.  9  hr.,  9  hr.  3  min.  17.62  sec. 

10.  9  P.M.  Dec.  31,  10  p.m.  Dec.  31,  11  p.m.  Dec.  31,  5  a.m.  Jan.  1, 
6  A.M.  Jan.  1. 


5.  2  :30  P.M.,  1:30  p.m. 

6.  I  hr.  9  min.  21  sec.  p.m. 

7.  Standard,  9  min.  42.72  sec. 

8.  6  min.  25.1  sec. 


10  ANSWERS 


Page  83 


1.  4  min.  6y^^  sec,  5  min.  4  sec. 

2.  44  min.  13.9  sec,  5  hr.  49  min.  28f  sec. 

3.  3  hr.  14  min.  43^1  sec,  6  hr.  4  min.  20 J  sec. 

4.  54  min.  33yLj.  sec,  2  hr.  19  min.  15||  sec. 
6.   11  A.M.,  10  hr.  50  min.  17.28  sec.  a.m. 

6.  11  hr.  54  min.  59.2  sec.  a.m.,  10  hr.  54  min.  59.2  sec.  a.m. 

7.  32  min.  32^8^  sec.  13.  1  hr.  41  min.  4f  sec. 

8.  1  hr.  1  min.  50  sec.  14.  2  hr.  11  min.  13^*3  sec. 

9.  29  min.  35i  sec.  15.  25  min.  9i-\  sec. 

10.  1  hr.  36  min.  40i  sec.  16.  3  hr.  13  min.  5^2^  sec 

11.  1  hr.  10  min.  49  sec.  17.  4  hr.  13  min.  18  sec 

12.  33  min.  18|  sec  18.  36  min.  55  sec. 

19.  46°  2^  21.  79°16M5^  23.  124°  46M5'^ 

20.  151°  r.  22.   107°  19'  30''.  24.  87°  43'  45". 

Page  86 

1.  $560.80.  4.  $308.50,  $1543. 

2.  1246.24.  5.  $26.25. 

3.  57^%,62i%,27^T%i26f%,15f%,41|%.    6.  $579.39, $255.75,  $325.50. 

7.  $142.50.  11.  ij.  16.  |.  19.  f  23.  fjf      27. 

8.  1533.  12.  f.  16.  |.  20.  ^%%. 

9.  if-  13.  ^%.  17.  1.  21.  |f§.  25.  17. 
10.   I  14.  ^V  18.  33^.  22.  tVoV  26.  $37.07. 

Page  88 

1.  292  da.  4.  3933.        7.  $161.20,  $145.08. 

2.  $55.80.  5.  4  da.        8.  $656.08. 

3.  $25.69,  $51.38,  $12.85,  $64.23.     6.  $252.        9.  235. 

Page  90 

1.  331%.  3.  20%.  5.  16f%.  7.  90%. 

2.  11J%.  4.  15%.  6.  12,626.12  sq.  mi.  8.  15%. 

Page  91 

1.  13^%.  3.  26ff%.  5.  11.98  +  %.  7.  18^^^%- 

2.  20|%.  4.  5if%.  6.  21f%. 


1.  15. 

4.  21f%. 

2.  50%. 

6.  25%. 

3.  10.21. 

6.  $20. 

ANSWERS  11 

Page  92 

7.  The  first,  23^%- 

8.  15. 

9.  $135.20. 

Page  95 

1.  $42.50,117.        3.  $29.25,  $17.55.   5.  $175.   7.  400  ft.      9.  11%. 

2.  $35.75,  $28.60.  4.  $324,  $113.40.    6.  $225.   8.  28,200.  10.  $1650. 

Page  96 

1.  $3162.50,  $3080.  5.  $891,  $907.50,  $924,  $899.25. 

2.  $3080,  $3220.  6.  $13,175. 

3.  $371,  $367.50,  $362.25,  $365.75.  7.  12^%. 

4.  238.  8.  $8308.75. 

Page  97 

1.  3}%.  2.  60%.  3.  $12.50.  4.  31J  sq.  mi.  6.  $8.40. 

Page  98 

1.  60%,  166f%,  37i%,  621%.  2.  22,500,  50,000. 

3.  $175.  4.  $124.08.  6.  $62.50,  $92.50. 

Page  100 

1.  $48.13.  5.  $21.95.  9.  $261.25. 

2.  $593.75.  6.  $25.08.  10.  $372.75. 

3.  $88.73.  7.  $105.08.  11.  $546.75. 

4.  $38.96.  8.  $268.54,  $219.71,  $292.95. 

Page  101 

1.  $21.98.       4.  $28.27.       7.  $18.85.       10.  $106.91.       13.  $622.71. 

2.  $58.04.       5.  $9.19.         8.  $45.10.       11.  $78.07. 

3.  $43.90.       6.  $37.08.       9.  $33.98.       12.  $36.28. 


12  ANSWERS 

Page  104 

1.  $12.80.  9.  $221.58.  17.  $1933.29. 

2.  $7.  10.  $252.62.  18.  $2560.16. 

3.  $7.88.  11.  $271.25.  19.  $345.14. 

4.  $23.13.  12.  $17.73.  20.  $466.61. 

5.  $15.40.  13.  $33.16.  21.  $408.50. 

6.  $35.25.  14.  $84.40.  22.  $147.33. 

7.  $90.30.  16.  $187.43.  23.  $263.18. 

8.  $46.43.  16.  $380.67.  24.  The  second  plan,  $4.20. 


Pages  105,  106 

1.  123  da.  8.  $11.59.  15.  $7.01.  22.  $645.40. 

2.  158  da.  9.  $18.19.  16.  $1003.96.  23.  $696.18. 

3.  110  da.  10.  $8.22.  17.  $152.44.   .  24.  $844.80. 

4.  224  da.  11.  $7.48.  18.  $76.73.  25.  $1042.66. 


5.  122  da.  12.  $4.45.  19.  $455.89.  26. 

6.  127  da.  13.  $10.27.  20.  $283.07.  27.  $7.64. 

7.  $4.90.  14.  $8.99.  21.  $896.15.  28.  $471.59. 


Page  107 

1.  $37.50.  3.  $3.80.  5.  $7.37.  7.  $5.38. 

2.  $52.90.  4.  $80.60.  6.  $364.50.  8.  $18.75. 
9.  $10.08,  same.                              10.  $12.01,  $11.63,  $11.88. 

Page  108 


1. 

$61.15. 

9. 

$2.49,  $2.53. 

2. 

$584.40,  $596.28,  $578.46,  $566.58. 

10. 

$4.75,  $4.81. 

3. 

$15.33,  $15.12. 

11. 

$46.23,  $46.88. 

4. 

$1.82,  $3.95. 

12. 

$34.72,  $35.20. 

5. 

$50  -  $49.32  =  $0.68. 

13. 

$17.17,  $17.41. 

6. 

$6.42,  $6.51. 

14. 

$40.11,  $40  at  60  da., 

7. 

$34.19,  $34.67. 

$40.67  at  61  da. 

8. 

$2.37,  $2.41. 

16. 

$13.95,  $14.15. 

ANSWERS 

13 

Page  109 

1. 

5%.               6. 

4%. 

9.  4%. 

13. 

3%. 

17.  4%. 

2. 

6%.               6. 

4%. 

10.  3|%. 

14. 

3|%. 

18.  4%. 

3. 

4%.               7. 

6%. 

11.  3%. 

15. 

2%. 

19.  6%. 

4. 

5%.               8. 

4%. 

12.  51%. 
Page  110 

16. 

4i%. 

20.  6%. 

1. 

2  yr.  6  mo. 

6. 

1  yr.  6  mo. 

11. 

16  yr.  8  mo. 

2. 

2  yr.  6  mo. 

7. 

1  yr.  5  mo.  3  da. 

12. 

2  yr.  6  mo. 

3. 

2  yr.  7  mo. 

8. 

2yr. 

13. 

11  yr. 

4. 

1  yr.  8  mo. 

9. 

1  yr.  2  da. 

14. 

14  yr. 

5. 

1  yr.  9  mo. 

10. 

4  mo. 

Pages  112,  113 


1. 

•141.33.                4. 

$24.59.                 7.  $102.62.                   10.  4%. 

2. 

$126.                    5. 

$56.11.                 8.  $1022.71.                 11.  3i%. 

3. 

$2.68.                  6. 

$105.75.               9.   5%. 

12.  3^%. 

13. 

1  yr.  2  mo.  10 1?  da.          17.  3  yr.  6  mo. 

21.  The  first,  $3.13. 

14. 

2  yr.  4  mo.  28  da. 

18.  $840. 

22.  3if%. 

15. 

5yr. 

19.  $30. 

23.  $405. 

16. 

1  yr.  6  mo.  15  da. 

20.  $55  less. 

24.  $1035. 

25. 

$3327.50  loss. 

27.  Net  income  $190  in  each  case. 

26. 

$5302.50. 

28.   19f%. 
Page  114 

1. 

4JA.,1000. 

3.  7200. 

5.  10  da.,  $18. 

2. 

266f  lb.,  8|lb. 

4,  1920,  40. 

6.   1500. 

Pages  115,  116 


1. 

12i%. 

7. 

$0.25. 

14. 

$6,  25%. 

2. 

$440,  17i%. 

8. 

$3.59. 

15. 

$1.44  gain, 

8if% 

3. 

11t^3%,  gain. 

9. 

38f%. 

16. 

$2.88  gain. 

4. 

37i%,  56]%. 

10. 

$59.40,  30|%. 

17. 

$42,  $3.99. 

5. 

$16.31,  gain. 

11. 

$0.29. 

6. 

$13.40,  $13.10, 
113.20,  $13.35. 

12. 
13. 

$25.50,  101f%. 

12,  4J%. 

14 


ANSWERS 


Page  118 


1. 

32.83. 

4. 

217.98. 

7. 

3.65. 

10. 

1.1. 

13. 

9.775. 

2. 

457.104. 

5. 

65.1. 

8. 

8.37. 

11. 

2.1. 

14. 

1.34f. 

8. 

19.032. 

6. 

2.38. 

9. 
Page 

0.51. 
120 

12. 

8. 

15. 

0.9f 

1.  187,  341. 

2.  169,  533. 

3.  189,  261. 

4.  476,  574. 

5.  6.51,  6.72. 

6.  4.41,  11.13 


7.  33,  55,  77. 

8.  65,  91,  117. 

9.  147,  231,  273. 

10.  583,  689,  901. 

11.  8.19,10.01,15.47. 

12.  .891,1.701,1.863. 


13.  12.07,13.49,14.91. 

14.  260,  130. 

15.  $1600,  $1200. 

16.  328.75,  $40. 

17.  $13.20,  $12.70. 


1.  22.6ff 

2.  4.135. 

3.  15.7xV 


Page  121 


4.  0.24. 

5.  2.003x^3-. 

6.  1.281^. 


13. 


771 


9.  1.5. 
5473. 


10.  3120. 

11.  106. 7ff: 

12.  1.4^\. 


Pages  122,  123 


1. 

46  bbl. 

6. 

4. 

11. 

5. 

2. 

$2142. 

7. 

21if  sec. 

12. 

8  min.  23.2  sec. 

3. 

302  ft. 

8. 

12  min.  40  sec. 

13. 

29  min.  59^  sec. 

4. 

1011  ft. 

9. 

75  mi. 

14. 

$14.70. 

5. 

4hr. 

10. 

3. 

16. 

$4. 

Pages  126,  127 


1. 

15  bbl. 

5. 

5f. 

9. 

5i  da. 

14. 

5  da. 

18. 

40. 

2. 

2f  bu. 

6. 

$132.50. 

10. 

6,2. 

15. 

4|  da. ,, 

19. 

$17.50. 

3. 

$992.79. 

7. 

50. 

11. 

31i|fda. 

16. 

'  $48,  $35) 

20. 

14. 

4. 

$7.20. 

8. 

$9.37i 

12. 
13. 

0.75  mo. 
180  T. 

17. 

loT 

21. 

1350. 

ANSWERS  16 

/ 

Pages  128-130 


1. 

1t¥AA. 

9.  $26.25.                   17.  12  lb.  9f  oz. 

2. 

21ft. 

10.  $10.                        18.  19  lb. 

3. 

$3. 

11.  $138.                      19.  84%. 

4. 

$4.55. 

12.  242Jglb.               20.  6,445,312^  lb.. 

5. 

$0.82  J. 

13.  6300.                                 2,352,539,062i  lb. 

6. 

$8.05. 

14.   12,675,000.            21.   189  bbl.,  891  bu. 

7. 

$30,371. 

15.  2,281,500.              22.  2,038,405,600  bu. 

8. 

$11.25. 

16.  20.24  oz.                23.  $17.50. 

24. 

$450,000,000, 

$45,000,000.           27.  15  bu.,  $58,500,000. 

25. 

34  bu.,  25)^,  $8.50.                         28.  lOi  T. 

26. 

$1100. 

29.  30  min. 
Pages  132-137 

1. 

M*%,  99ifi%. 

6.  28,224. 

2. 

3.125  lb.,  3.125  lb.,  243.75  lb.        7.  80  lb.,  300  lb.,  60  lb.,  225  lb. 

3. 

299.04  lb. 

8.  875  1b.,  950  1b.,  175  1b. 

4. 

139.32  lb. 

9.  1075  lb.,  800  lb.,  125  lb. 

5. 

138,750. 

10.  $12.07i. 

11. 

262.5  lb.,  37.5  lb.,  112.5  lb.,  337.5  lb.,  700  lb.,  100  lb.,  300  lb.. 

900  lb.,  1050  lb.,  150  lb.,  450  lb.,  1350  lb. 

12. 

$18.82. 

17.  137^V%-                      22.  21,0001b. 

13. 

$18.72. 

18.  96  bu.,  18f  bu.         23.  31%. 

14. 

$16.86. 

19.  37.625  1b.                  24.  66  1b. 

15. 

$60.50. 

20.  43.8951  lb.                 25.  $46. 

16. 

269A%. 

21.  $10,531.                    26.  $0.54,  the  second. 

27. 

A.  152  lb.,  44.08  lb.,  $12.34.       B.  185  lb.,  62.9  lb.,  $17.61. 

C.  277  lb.,  74.79  lb.,  $20.94.      D.  114  lb.,  34.2  lb.,  $9.58. 

E.  212  lb.,  55.12  lb.,  $15.43.       F.  421  lb.,  147.35  lb.,  $41.26. 

G.  521  lb.,  166.72  lb.,  $46.68. 

a 

h                     c                     d 

28. 

1.  672  lb. 

168  lb.             196  lb.             $45.08. 

2.  672  lb. 

168  lb.            196  lb.            $45.08. 

3.  528  1b. 

132  lb.            164  lb.            $35.42. 

4.  408  1b. 

1021b.            1191b.            $27.37. 

5.  528  1b. 

132  lb.            154  lb.            $85.42. 

29. 

30.72  lb.,  35.84  lb.                           31.  5  lb.                 33.  181/^  lb. 

80. 

4%,  34  1b.,  39| 

lb.,  $9.92.               32.  6001b. 

16 


ANSWERS 


Pages  139,  140 

1.  $1200.  3.  83i%.  5.  300  da.  7.  $1690. 

2.  $1150.  4.  $1350.  6.  $2.  8.  $9  decrease. 
9.  $4,  second  plan.  10.  $5.16,  second  place.  11.  $270,  $324,  $450,  $600. 

12.  $4.60,  $4.37,  $4.83,  $6.13i,  operating  department.  13.  $25. 

Pages  141,  142 


1. 

2. 

$91.25.        3.  $375. 
$465.           4.  $231. 

5.  $168.30.        7. 

6.  $911.10.        8. 

Page  144 

$107.18.         9.  $73.20. 
$1852.50.      10.  $167. 

1. 
2. 
3. 

4. 
5. 
6. 

7. 
8. 

$3000,  $3038.74. 
$4720,  $4764.06. 
$3920,  $3937.02. 
$2520,  $2532.40. 
$3080,  $3095.15. 
$1933.75,  $1940.25. 
$713.07,  $717.77. 
$12,400,  $12653.19. 

9.  $502.09,  $507.42. 

10.  $312.69,  $314.40. 

11.  $225.23. 

12.  $324.73. 

13.  $731.59. 

14.  $765.41. 

15.  $900.94. 

16.  $541.21. 

Page  146 

17.  $1093.08. 

18.  $1126.16. 

19.  $2143.72. 

20.  $3152.83. 

21.  $9.46  more  at 

simple  interest. 

22.  $35.13. 

23.  $1380.86. 

1. 
2. 

$509.            3.  $524.23.       5.  $930.75.       7 
$1176.92.     4.  $2462.35.     6.  $211.44.       8 

.   715.23.      9.  '$246.80. 
.  $1668.      10.  $272. 

Page  148 

1. 
2. 

$155.25. 
$156. 

3.  $159.23. 

4.  $517.43. 

Page  151 

5.  $810.40. 

6.  $848.74. 

1. 

2. 

3. 

4. 
13. 
14. 
16. 

$4.38,  $870.62. 
$12.19,  $962.81. 
$2.13,  $422.87. 
$21.40,  $2546.60. 
$6.25,  discount. 
$3.38,  discount. 
$18.75,  discount. 

5.  $12.50,  $1237.50.        9.  $15.94,  $4234.06. 

6.  $18.75,  $1481.25.      10.  $1.63,  $323.87. 

7.  $32.06,  $2532.94.      11.  $3.56,  $423.94. 

8.  $44.69,  $3205.31.      12.  $0.99,  $236.51. 

16.  $1500. 

17.  $22.50,  $1477.50;  $15,  $1485. 

18.  $700,  discount  =  $3.50. 

ANSWERS 


17 


Page  153 

1.  $0.76,  $300.25;  |0.80,  1300.20. 

2.  $6.86,  $799.81;  $6.99,  $799.68. 

3.  $2.78,  $552.72;  $2.87,  $552.63. 

4.  $1.39,  $331.74;  $1.43,  $331.70. 

5.  $5.03,  $999.97;  $5.19,  $999.81. 

6.  $21.59,  $1252.54;  $21.77,  $1252.36. 

The  second  set  of  answers  in  Exs.  1-6  are  the  results  obtained  when 
both  the  first  and  last  days  of  the  discount  period  are  counted. 

7.  $31.25,  $3718.75. 

8.  $35.21,  $4189.79. 

9.  $99.75,  $9400.25. 

10.  $65.63,  $7434.37. 

11.  $54.57,  $4170.43. 

12.  $86.41,  $5488.59. 

13.  $34.38,  $7465.62. 

14.  $26.13,  $4723.87. 

15.  $0.21,  $42.29. 


16. 

$0.14,  $27.46. 

26. 

$4.69,  $370.71. 

17. 

$0.18,  $35.32. 

27. 

$31.97,  $2718.03. 

18. 

$0.14,  $28.61. 

28. 

$38.07,  $3236.93. 

19. 

$1.26,  $124.24. 

29. 

$45.82,  $4714.18. 

20. 

$2.75,  $272.50. 

30. 

$26.42,  $2718.58. 

21. 

$5.63,  $369.87. 

31. 

$6.37,  $1538.63. 

22. 

$6.76,  $443.99. 

32. 

$5.05,  $1569.95. 

23. 

$1.91,  $455.59. 

33. 

$1250. 

24. 

$1.23,  $295.27. 

34. 

$1747.07. 

26. 

$3.60,  $284. 

1.  $393.75. 

2.  $337.28. 

3.  $102.52. 


Pages  155,  156 


4.  $651.97. 

5.  $191.96. 

6.  $178.85. 


7.  $211.08. 

8.  $476.18. 

9.  $453.49. 


13.  $297.09. 


10.  $375.58. 

11.  $60.20. 

12.  $408.34. 


1.  $189.95. 


Page  157 
2.  $106.42. 


1.  $1.34,  $0.67,  $2.68. 

2.  e$5.67. 


Page  159 

3.  .$5.42,  $1.17. 

4.  $5.87,  $8.80. 
6.  $1.03,  $0.20. 


5.43,  $12.86. 
3.74,  $11.22 


18 


ANSWERS 


1.  165.87.  . 

2.  1540. 


3.  .$95.42. 

4.  $62.04. 


Page  161 

5.  1121.87. 

6.  $345. 


7.  $3317.28. 

8.  $3375.25. 


9.  $304.77. 


1.  $187.70. 

2.  $29.30. 


Pages  162,  163 


3.  $1.39. 

4.  $1.35. 


6.  $63.07. 
6.  $4.40. 


7.  $4.65. 

8.  $481.41. 


Pages  165,  166 


8.  $240,  $315. 

9.  $11.10,  $14.40. 

10.  $5446.45,  $3853.55. 

11.  $175,  $2325. 

12.  $3925,  $2475. 

13.  $3900,  $900,  $2400. 
14. 


1.  $31.05,  $56.25,  $65.70. 

2.  $440,  $670,  $330. 

3.  $810,  $975,  $615. 

4.  $75,  $54,  $66. 

5.  $210,  $315,  $560. 

6.  $110,  $88,  $6d. 

7.  $65.10,  $36. 

15.  $8.16,  $6.36,  $10.20. 

Page  169 

1.  $300.60.  6.  $2750,  $2.75. 

2.  $3203.20,  $2501.25.  7.  $3750,  $1.50. 

3.  Add  15;^,  25j^,  10^,  30)^,  SOf.    8.  $250.25,  $150.15,  $100.10,  $350.35. 

4.  $2751.10.  9.  Draft,  10)^. 

6.  0.3%.  10.  Registered  letter,  2f. 


.45. 


Pages  170,  171 


1.  $749.25.       3.  $149.70. 


1%%' 


5.  i%- 

6.  $74.85. 


8.  2V%. 

9.  $249.75. 


10.  $99.90. 

11.  $0.75. 


1.  $3756.70 

2.  $3496.50. 

3.  $751.50. 

4.  $6753.38. 


Page  173 


5.  $2452.45. 

6.  $17,465. 

7.  $5161. 

8.  $3408.50. 


9.  Discount,  i%. 

10.  Discount,  ^%. 

11.  $249.75. 

12.  $2447.50. 


13. 
14. 


$379.75. 
$3240. 


ANSWERS 


19 


Page  175 


1. 

720d. 

11. 

£3.2. 

21. 

92.75  M. 

31.  $17.85. 

2. 

528d. 

12. 

£6.225. 

22. 

17,500  pf. 

32.  $29.75. 

3. 

786d. 

13. 

2500 

c. 

23. 

20,000  pf. 

33.  $892.50. 

4. 

44d. 

14. 

3700 

c. 

24. 

1075  pf. 

34.  40  M. 

5. 

219d. 

15. 

3530 

c. 

25. 

$365.25. 

35.  60  M. 

6. 

1214d. 

16. 

2.75  fr. 

26. 

$331.16. 

36.  300  M. 

7. 

8.66|s. 

17. 

4.75  fr. 

27. 

$80.36. 

37.  $16.41. 

8. 

9.25s. 

18. 

12.75  fr. 

28. 

£8. 

38.  $44.39. 

9. 

66.75s. 

19. 

3.5  M. 

29. 

£5. 

39.  $144.75. 

10. 

£2.1. 

20. 

4.8  M. 

30. 

£9. 

Page 

177 

1. 

$433.50. 

5.  650  fr. 

9.  Demand  draft 

2. 

.$58.75. 

6.  322.12  M. 

$1.37  better. 

3. 

$176.02,  $145.51. 

7.  $610.73. 

10.  $130.69. 

4. 

£15. 

8.  $111. 
Page 

180 

1. 

0.2763  m. 

12. 

20.94  mi. 

24. 

184.2516  in. 

2. 

4.764  m. 

13. 

3.168  mi. 

25. 

1358.265  in. 

3. 

29.38  m. 

14. 

1.7856 

mi. 

26. 

1.114171  in. 

4. 

4.862  km. 

15. 

0.88686 

mi. 

27. 

118.11  in. 

5. 

0.12758  km. 

16. 

55|  ft. 

28. 

2.7559  in. 

6. 

0.628341  km, 

17. 

208  ft. 

29. 

659.75  ft. 

7. 

78.33L  km. 

18. 

351  ft. 

30. 

121.875  ft. 

8. 

44.16f  km. 

19. 

224.055  ft. 

31. 

125.4  mi. 

9. 

3.331  km. 

20. 

97.045  ft. 

32. 

106.8  mi. 

10. 

450.6  mi. 

21. 

264.212  ft. 

33. 

61  fr.  20  c. 

11. 

171.6  mi. 

22. 

1850.39 

'  in. 

34. 

27. 9f  mi. 

23. 

127.5588  in. 

Page 

181 

1.  7,500,000,000,000  cm2.  3.  42.96  cm2. 

2.  370,000  cm2.  4.  62,500  cm2. 

5.  80,683,750  A.,  using  2J  A.  =  1  ha. 


Page 

182 

1. 

2. 

19,750  m8. 
0.00042765384  m3. 

3. 

4. 

1161.6c 
Ims. 

Jms. 

5. 
6. 

100  m3. 

1  m3. 

Page 

184 

1. 
2. 
3. 
4. 
5. 
6. 
7. 

170  kg. 
10  kg.    • 
3.275  kg. 

7012^\  kg. 
22  kg.. 
7.275  kg. 
IOOIt^t  kg. 

8. 

9. 
10. 
11. 
12. 

13. 

3  kg. 

79  kg. 

77  1b. 

200  5-ct.  pieces. 

0.0352  oz., 

0.0022  lb. 
55  1b. 

14. 
16. 
16. 
17. 
18. 
19. 
20. 

11^  t.,  86.7  t. 
30.94  t.,  8.4  t. 
28.2906  kg. 
0.6075  t. 
3174.8706  g. 
521.1  g.,  0.5211kg. 
165  lb. 

Page 

186 

1. 
2. 
3. 
4. 
5. 
6. 

7.224  kg. 

5.81  kg.,  12.782  lb. 

11,811  in.,  984.25  ft.,  0.3  km. 

337.75  g.,  5201.35  grains. 

2.25  kg.,  4.95  lb. 

2929.5  g. 

7. 

8. 

9. 
10. 
11. 
12. 

5138  g. 

29.625  kg. 

160.2  kg. 

0.06  ha.,  0.124  A. 

0.77  1b.,  12.32  oz.,  0.35  kg. 

30,000  kg.,  18751b. 

Page 

189 

1.  $1052.18. 

Pages  190,  191 

1. 
2. 

3. 
4. 

42,23%. 
22M%,  18, 

28H%. 
4Jff%. 

2A%. 

?T%, 

5. 
6. 

7. 
8. 
9. 

3566f%. 
32%. 

40A%. 

$92,049,300. 

10. 
11. 
12. 

13. 

$229,926,355.40. 
$53,590,000, 
$179,410,000. 

$9,180,000. 

Page 

192 

1. 
2. 

0.0086||%, 
$7.80. 

3. 
4. 
6. 

9.1%.                          6 
$0.08,  $1,826,512.    7 
$2000,  $296. 

.  507,500  mi.,  475,020,000  mi. 
.  $514.89. 

ANSWERS  .  21 


Pages  193,  194 

1.  ^3,220,000,  5.  24  hr.  11.  72  hr. 

13,590,000.  6.  15,000.  12.  20,  20. 

2.  474  lb.  7.  23,  4/3%.  13.  27,200  T. 

3.  459  lb.  8.  23  knots.  14.  $696,  |8352. 

4.  4,000,000  1b.,  9.  10.1  in.  15.  10,420|  ft. 

31,120,0001b.  10.  130,206  1b. 


Page  196 

1.  $1961 M,  ad  valorem.    4.  $131.49.    7.  $144.75,  $36.19,  $180.94. 

2.  $1050,  specific.  5.  $1620.       8.  $1905.88,  $762.35,  $2668.23. 

3.  $127.84.  6.  $2830.       9.  $790.75. 


Page  197 

5.  $39.  9.  $197.  13.  $64. 

6.  $216.  10.  $75.  14.  $262.50. 

3.  $1125.  7.  $37.50.  11.  $278.50.  15.  $139.50. 

4.  $62.50.  8.  $80.  12.  $15.  16.  $27. 


Page  199 

1.  $40.63.  6.  $55.60.  11.  $0.0045.  16.  $9,125,000. 

2.  $1125.  7.  $0,004.  12.  $0,006.  17.  $19,035. 

3.  $0.0055.  8.  $0,003.  13.  $2,750,000.  18.  $47,625. 

4.  $64.75.              9.  $0.0055.          14.  $3,500,000.  19.  $39,875. 
6.  $0.0075.         10.  $0,003.            15.  $8,250,000.  20.  $83,070. 


Page  200 

The  second  answer  is  the  net  tax  plus  the  collector's  1%,  calling  a 
fraction  of  a  cent  one  cent. 

1.  $35.75,  $36.11.          6.  $66,  $66.66.  9.  $171.05,  $172.77. 

2.  $48.13,  $48.62.          6.  $90.75,  $91.66.  10.  $127.88,  $129.16. 

3.  $26.81,  $27.08.          7.  $134.20,  $135.55.  11.  $103.82,  $104.86. 

4.  $42.21,  $42.65.          8.  $129.25,  $130.55.  12.  $248.88,  $251.37. 


22 


ANSWERS 


Pages  203,  204 

1.  $23.75.  8.  $202.13. 

2.  $30.80.  9.  $1.54,  $0.51. 

3.  $43.13.  10.  $1.20,  $0.40. 

4.  $160.  11.  $10,000. 

5.  $75.  12.'  $10,500,  $16,800. 

6.  $3500.  13.  $6050. 

7.  $2052.  14.  $31.25,  $1500. 

15.  3-year  policy,  $10.50. 


16.  $5880. 

17.  $2972.98. 

18.  $7785. 

19.  $25,000. 

20.  $1200,  $3. 

21.  161- yr. 


1.  $9000. 

2.  $44,900. 


Page  205 

3.  $123.35. 

4.  $102,  $163.20. 


5.  $54,  $162,  $108. 

6.  $16.92,  $25.38,  $84.60. 


Pages  208,  209 


1. 

2. 
3. 
4. 
6. 

$136.95. 
$410.40,  $4104. 
$2739. 
$171,  $3420. 
$243.75,  $4875. 

6.  ^6,  $82.25. 

7.  $263.60,  $6590. 

8.  $4076. 

9.  $2739,  $3834.60. 

10.  $24.60. 

11.  $951.50. 

Pcige  211 

12. 
13. 
14. 
15. 
16. 

$1912,  $922. 

$402. 

$1072.80. 

$331.20. 

$1917. 

1. 
2. 
3. 

15,000.      4. 
$1,250,000.   5. 
$500.       6. 

$270.       7.  $2,750,000. 
$135.       8.  $12,500, 
li%.           $250. 

9.  2|%. 
10.  5%. 

Page  213 

1. 
2. 
3. 

$9553.13.    4. 

$3415.63.    5. 

$8512.50.    6. 

13. 

$7843.75.     7.  $10,730. 
$16,387.50.   8.  $31,937.50. 
$43,125.     9.  $29,553.13. 
68J.       14.  40. 

10.  $44,468.75. 

11.  $20,667.50. 

12.  $17,085. 

ANSWERS 


23 


Pages  214,  215 


1. 

$150. 

10. 

$131.25  loss. 

19. 

$287.  50  loss. 

2. 

1306.25. 

11. 

$12.50  gain. 

20. 

$100  loss. 

3. 

12.50  loss. 

12. 

$50  gain. 

21. 

124|. 

4. 

116,467.50. 

13. 

$106.25  loss. 

22. 

142|. 

5. 

$31.25  gain. 

14. 

Neither  gain  nor 

23. 

$24,393.75. 

6. 

$125  loss. 

loss. 

24. 

250. 

7. 

$275  loss. 

15. 

$18.75  gain. 

25. 

200. 

8. 

$75  gain. 

16. 

$93.75  gain. 

26. 

$272. 

9. 

Neither  gain  nor 

17. 

$68.75  gain. 

loss. 

18. 

$87.50  loss. 

Pages  217,  218 

1.  $7218.75,  $7706.25,  $5146.88,       12.  The  same. 


$7500. 

2.  4%. 

3.  5%  stock  @  139J. 

4.  Same. 

5.  31%. 

7.  5^%  note. 

8.  7%  stock  @  149|. 

,  9.  5%  bond  @  121,  jmj%. 

10.  The  same. 

11.  The  same. 


13.  5%  bond  @  108,  3f  T%. 

14.  6%  bond  @  140,  8VV%. 

15.  31%  bond  @  107,  ^ffy%. 

16.  5%  bond  @  111,  2i^%. 

17.  The  same. 

18.  4%  bond  @  86,  ^2^0^%. 

19.  The  same. 

20.  5%  stock  @  95,  3-\%. 

21.  5%  stock  @  114,  7f  J^%. 

22.  $1487.50,  stock;  $1103.75,  at 

interest. 


23.  $83.79  gained  by  stock. 


1.  $2760. 


Page  219 
2.  $84.38.  3.  $33.75.  4.  $318.75. 


1.  $13,732.50. 

2.  $5283.75. 


Page  220 

3.  $184,650.  5.  $147,000. 

4.  $7000.  6.  $150. 

9.  $540  gain. 


7.  $93.75  gain. 

8.  $53,345. 


24  ANSWERS 


Pages  221-223 

1.  120.  2.  Wage  earners,  $285;  others,  $1511. 

3.  Materials,  $181,170,000;  labor,  $56,430,000 ;  salaries,  $5,940,000; 

miscellaneous,  $17,820,000;  profit,  $35,640,000. 

4.  White  pine,  543,950  M;  hemlock,  247,940  M;  spruce,  106,260  M; 

yellowpine,  703,340  M ;  oak,  323,840  M ;  other  woods,  604,670  M. 
6.  $10,373,000.  8.  $172,000,000.  11.  31%. 

6.  $3,542,000.  9.  $222,000,000.  12.  376,441  doz. 

7.  293^%.  10.  $98,000,000.  13.  Decreased,  $30. 

14.  Population,  84% ;  ice,  345\\%.       16.  $255,280,000. 

15.  $786,600,000.  17.  10)z^. 

18.  Canada,  103,105,926  bu. ;  U.S.,  687,372,840  bu. ;  both,  790,478,766 

bu.  20.  21,900,000  bbl. 

19.  42,500,000  cu.  ft.  21.  4/3-%,  4Jf%,  4^^%.  H7o' 

Page  224 

1.  $112,  $109.20.  5.  672,000,000  lb.,  436,800,000  lb., 

2.  $4,  $4.30.  60.6  +  %,  39.4  -  %. 

3.  1.775%.  6.  5,717,333  T. 

4.  $3,258,048.60  @  $4.10.  7.  322. 

Page  225 

1.  $0.47+.  3.  7301b.  5.  2J  in. 

2.  1126J  lb.  4.  275,968  T.  6.  290,400  long  T. 
7.  $2.47  or  $2.52,  depending  on  how  cross  pieces  run. 

Page  226 

1.  2437.  4.  944:  5775  =  nearly  1:6.12.    7.  SftllyVin. 

2.  255,000,000  cu.  ft.    5.  5.  8.  $761,400. 

3.  1750  cu.  ft.  6.  1.44 -m.  9.  $25,698,336. 

Page  227 

1.  691.15  mi.  4.  2590. 

2.  2850  passengers,  342  crew.  5.  5600  T.,  12,544,000  lb. 

3.  41yV5%.  6.  15  times,  3f  times. 


ANSWERS  25 

Pages  228,  229 

3.  39i°F.,  16f  C. 
2.  1.8°.  4.  29.871  in.,  29.433  in. 

6.  4,515,720  T.,  1,517,340  T.,  1,052,700  T.,  3,121,800  T.,  2,403,060  T., 
1,996,500  T.,  2,983,860  T.,  3,397,680  T. 

6.  1,517,450  mi.  9.  1.765- mi.  12.  787.9872  T. 

7.  6.94375  lb.  10.  19,488  ft.  13.  1  mi.,  100  mi. 
8.80%.                               11.  44min.  14.13,392  1b. 

Page  231 


1. 

25.      6.  48. 

11.  6.4. 

16. 

2.1  in. 

21.  0.35  ft. 

26.  48.4  in. 

2. 

18.      7.  36. 

12.   121. 

17. 

66  in. 

22.  324  ft. 

27.   576  in. 

3. 

22.      8.  33. 

13.  2.2  in. 

18. 

125  in. 

23.  440  in. 

28.  512  in. 

4. 

27.      9.  8.1. 

14.   1.4  ft. 

19. 

77  yd. 

24.  420  ft. 

29.  520  ft. 

5. 

24.    10.  3.5. 

15.   1.5  ft. 

20. 

3.3  yd. 

25.  560  ft. 

30.   1440  in 

31.  96  rd., 

32  rd. 

33 

.  13  rd. 

32.   52  rd., 

,  104  rd.,  2. 

34 

.  68  rd.,  204  rd.,  3. 

Page  232 

1.  11.     2.  9.     3.  8.     4.  12.     5.  25.     6.  14.     7.  16.     8.  18.     9.  22  in. 


Page  236 

1. 

57. 

6. 

47. 

11. 

77. 

16.  87  ft. 

21. 

99 

yd. 

26. 

If 

2. 

61. 

7. 

53. 

12. 

79. 

17.  89  rd. 

22. 

ih 

27. 

Vv 

3. 

63. 

8. 

59. 

13. 

82  ft. 

18.  91  in. 

23. 

fi. 

28. 

tV- 

4. 

71. 

9. 

67. 

14. 

97  ft. 

19.  95  ft. 

24. 

I|. 

29. 

if 

5. 

41. 

10. 

73. 

15. 

85  in. 

20.  83  yd. 

25. 

n- 

Page  238 

1.  111.     4.  89.7.     7.  34.3.     10.  4607.     13.  1.41.       16.  2.828. 

2.  234.     5.  4.41.     8.  9.07.     11.  7008.     14.  2.236.     17.  3.316. 

3.  10.5.    6.  0.53.  '  9.  251.      12.  9812.     15.  2.645.     18.   12.649+rd. 


26  ANSWERS 

Pages  239,  240 

1.  86  ft.  6.  535  in.,  85  in.,  153  ft.     11.  16.40  rd.  16.  3.46  in. 

2.  2.82  ft.         7.  22  ft.  6  in.  12.  76.20ft.  17.  50  ft. 

3.  36.05  in.      8.  16  ft.  6  in.  13.  8.49  in.  18.  7.5  mi. 

4.  95  in.  9.43.60  ft.  14.  9.76  in.  19.  8.94  mi. 

5.  125  ft.        10.  88.24  ft.  15.  21.93  ft. 

Page  241 

2.  27.1488  in.  6.  127.260  ft.        10.  22.624  ft.  14.  5  ft. 

3.  46.3792  in.  7.  6.708  ft.  11.  3.535  ft. 

4.  965.762  ft.  8.  21.54  ft.  12.   10  in. 

5.  1060.500  rd.  9.  12.726  ft.  13.  3  in. 

Page  244 

1.  17.  4.  18.  7.  31.  10.  54.  13.  82.  16.  98. 

2.  19.  6.  24.  8.  36.  11.  61.  14.  91.  17.  84. 

3.  21.  6.  27.  9.   51.  12.  67.  15.  96.  18.  92. 

19.  95.        22.  2744.        24.  15,625.         26.  166,375.  28.  421,875. 

20.  99.        23.  9261.         25.  27,000.         27.  216,000.  29.  970,299. 

Page  247 

1.  13.         5.  42.  9.   52.        13.   109.        17.   169.  21.  46.3. 

2.  15.         6.  45.         10.  59.        14.  121.        18.  370.  22.  45.1. 

3.  14.         7.  46.        11.  63.        16.  138.        19.  378.  23.  0.486. 

4.  41.         8.  48.        12.   163.      16.   160.        20.  460.  24.  326. 

Page  249 

1.  214.3fin.        12.202.4  ft.  23.  40.8408  in.  34.  308  in. 

2.  151.8  ft.  13.  42  ft.  24.  8.79648  in.  36.  484  in. 

3.  1329fin.  14.  lSj\  it.  26.  13.728792in.  36.  572  in. 
4.16.06  ft.  15.31ft.  26.7.0686  ft.  37.  660  in. 
6.  169.4  ft.          16.  56  in.               27.  19.3732  ft.  38.  96.8  in. 

6.  20.02  in.         17.  245  ft.  28.  17  in.  39.   11  in. 

7.  14.74  ft.  18.  30f  ft.  29.  27  in.  40.  23.8  ft. 

8.  182.6  in.         19.  21.7  in.  30.  31  in.  41.  6.6  in. 

9.  18.92  ft.  20.  1.26  ft.  31.  29.9999+  ft.  42.  1.98  in. 

10.  42.4|ft.  21.0.154  ft.  32.   58+ ft.  43.  14.5  in. 

11.  55iift.  22.  53.4072  in.     33.44  ft. 


ANSWERS                                         27 

Page 

251 

1. 

2. 
3. 

4. 
5. 

SI  sq.  in. 

1386  sq.  ft. 

1386  sq.  ft. 

35  ft. 

39.82  in.,  126.12985 

sq. 

in. 

6.  7.7  in.,  3.85  in.,  46.585  sq.  in. 

7.  78.54  sq.  in.,  226.9806  sq.  in. 

8.  22  ft.,  38.5  sq.  ft. 

9.  7|in. 

Page  253 


1. 

10,875  cu.  in. 

8. 

9  in. 

15. 

100.34375  cu.  ft. 

2. 

0.3411  cu.  ft. 

9. 

8  in. 

16. 

2301.252  cu.  in. 

3. 

325.92  cu.  in. 

10. 

9f^. 

17. 

226,981  cu.  in. 

4. 

310.98  cu.  in. 

11. 

999.6  cu.  in. 

18. 

2885.794  cu.  in. 

5. 

178.383  cu.  ft. 

12. 

70.528  cu.  in. 

19. 

21  in.,  11  in. 

6. 

199.076  cu.  in. 

13. 

113.53076  cu.  in. 

20. 

7.5  in. 

7. 

8Hin. 

14. 

43.225  cu.  ft. 
Page  254 

1.  50,285f  cu.  ft.     3.  169,273||  gaj.     5.  2079  cu.  in. 

2.  46^2^  cu.  ft.        4.  144|  cu.  ft.  6.  2618  cu.  in.,  ll,455f  cu.  in. 

Page  256 

1.  105sq.  in.  4.  5092  sq.  ft.  8.  110  sq.  ft. 

2.  231sq.  in.  6.   188f  sq.  ft.  9.  27,456  sq.  ft. 

3.  62fsq.  in.  7.  244|  sq.  ft.  10.  1178^  sq.  ft. 

Page  257 

1.  160.332  cu.  in.       3.  600.9404  cu.  ft.  5.  21sq.  in.      7.  27  sq.  in. 

2.  3933.384  cu.  in.      4.  667.038  cu.  ft.  6.  21sq.  in.      8.  18sq.in. 
9.  93,537,284  cu.  ft.,  15,714,263,712  lb. 

Page  258 

1.  509.329^  cu.  in.,  1527.988  cu.  in.   5.  301f  cu.  in. 

2.  134.904  cu.  in.,  404.712  cu.  in.     6.  55,440  cu.  ft.,  415,800  gal. 

3.  407.484  cu.  in.,  1222.452  cu.  in.    7.  718f  cu.  in. 

4.  845.614  cu.  in.,  2536.842  cu.  in.    8.  18,102f  cu.  in.  =  lOJJcu.ft. 


28  ANSWERS 


Page  260 


1.  32  sq.m.  6.  692isq.  in.  11.  340sq.  in.  16.  115i  sq.  ft. 

2.  272sq.in.  7.  46.2}  sq.  in.  12.  294isq.in.  17.  764,000sq.  ft. 

3.  360  sq.  in.  8.  40.21|sq.in.  13.  10  in.  18.  960  sq.  ft. 

4.  140sq.  in.  9.  20.86  sq.  in.  14.  50  in.  19.  183i  sq.  ft. 

5.  176sq.in.  10.  10  sq.  ft.  15.  2040  sq.ft. 


Page  261 

1.  62 j%  sq.  in. 

2.  2,359,727,071,428^  sq.  mi.  ;  or,  say,  2,359,727,000,000  sq.  mi. 

3.  17Jff  sq.  in.  4.  2828f  sq.  in. 

Pages  262-265 

1.  56tVAcu.  in.  «3.  4.7724  sq.  in.  47.   18.76  rd. 

2.  4851  cu.  in.  24.  38  sq.  ft.  48.  15.84  yd. 

3.  4,190,476,1901$  25.  8.93  sq.  ft.  49.  2.74  in. 

cu.  mi.  26.  3037i  sq.  in.  50.  2.457  yd. 

4.  1767f  cu.  ft.  27.  0.0777  sq.  in.  51.  2.917  in. 

5.  36885V3V  cu.  ft.  28.  15.68  sq.  in.  52.  616  sq.  in. 

6.  221}  cu.  ft.  29.  3645  sq.  in.  53.  745.36  sq.  in. 

7.  53|f  cu.  ft.  30.  3.37i  sq.  ft.  54.  5003.46  sq.  in. 

8.  268,190,476,-  31.  18  in.  55.  13,034.56  sq.  ft. 

190if  cu.  mi.  32.  2.1  in.  56.   16,022.16  sq.  ft. 

9.  463.433}  cu.  in.  33.  3.4  in.  57.  26,832.96  sq.  yd. 
10.  776.046f  cu.  in.  34.  1.9  in.  58.  48,246.66  sq.  rd. 
11-AV^sq.  in.  35.  11  in.  59.  85,046.50  sq.  rd. 
12.  JIfsq.  in.  36.  17  in.  60.  174,896.26  sq.  yd. 
18.  ^^%\  sq.  in.  37.  64  in.  61.  9.899  in. 

14.  ^2_2_5^  sq.  in.  38.  6.4  ft.  62.  15.65  in. 

15.  8.2369  sq.ft.  39.  7.8  in.  63.  21  in. 

16.  15.3664  sq.  ft.  40.  8.4  in.  64.  23.216  ft. 

17.  306.25  sq.rd.  41.  0.44  in.  65.  24.249  ft. 

18.  0.1369  sq.  in.  42.  11  ft.  10  in.  66.  28.86  ft. 

19.  31.28  sq.ft.  43.  17.88  rd.  67.  3.569  yd. 

20.  46.72  sq.  in.  44.  13.076  ft.  68.  3.77  yd. 

21.  8if  sq.ft.  45.  19.62  ft.  69.  6.71yd. 

22.  3.86tV  sq.ft.  46.  12.369  in. 


ANSWERS  29 


70.  24,848,438if  cu.  in.,  411,852f  sq.  in. 

71.  21,323,020^^  cu.  in.,  371,913}  sq.  in. 

72.  1,023,065,476/^  cu.  in.,  4,910,7142  sq. 

73.  134,764.95  cu.  in.,  12,712.735.  sq.  in. 

74.  88,102.985  cu.  in.,  9576.41  sq.  in. 

75.  167,626.12  cu.  in.,  14,704.044  sq.  in. 


76. 

21.6  cu.  ft. 

84. 

109.184fjcu.  ft. 

92. 

86f  lb. 

77. 

93.48  cu.  in.. 

85. 

23.533f  cu.  ft. 

93. 

28  T. 

78. 

71.34  cu.  in. 

86. 

62.83  cu.  in. 

94. 

19.404  cu.  in. 

79. 

44.3||  cu.  ft. 

87. 

427.038f  cu.  in. 

95. 

2416f  f  lb. 

80. 

25.432  cu.  ft. 

88. 

28.1891  cu.  in. 

96. 

1,457,7775. 

81. 

439.899  cu.  in. 

89. 

498.968  cu.  ft. 

97. 

2^  in. 

82. 

225.254f  cu.  in. 

90. 

20i|f f f  cu.  ft. 

98. 

810fH  oz. 

83. 

2928.080^  cu.  ft. 

91. 

7O3Y7  cu.  ft. 

99. 

12303^V^  oz. 

100.  15.54  sq. 

ft. 

101.  2. 

102.  268,190,476,000  cu.  mi.,  201,143,000  sq.  mi. 
Pages  266-280 


1. 

35,  56. 

22. 

$550. 

43. 

41  ft. 

2. 

5,  35. 

23. 

66  ft. 

44. 

25  ft. 

3. 

140. 

24. 

$12.50  loss. 

45. 

127.27+ ft. 

4. 

487,  296. 

25. 

20%,  16f%. 

46. 

100.62  ft. 

5. 

740t\  lb. 

26. 

20,558,000  bbl. 

47. 

160. 

6. 

$140.40. 

27. 

5tV- 

48. 

3  hr.  30  min. 

7. 

129.661  lb. 

28. 

769.692  sq.  ft. 

49. 

128. 

8. 

$5.04. 

29. 

2. 

50. 

70Ahr.     • 

9. 

66f%. 

30. 

61  hr. 

51. 

10  hr. 

10. 

23xV%. 

31. 

1  yr.  2  mo. 

52. 

$1250,  $1750, 

11. 

V  llf'. 

32. 

51  sec. 

$1500. 

12. 

1,369,028*  T. 

33. 

2f  da. 

53. 

8.8  lb. 

13. 

36|4sq.in. 

34. 

80  da.,  lOff  da. 

55. 

$2.17. 

14. 

12  da. 

35. 

5  da. 

56. 

6T. 

15. 

24,942,881,6001b. 

36. 

76. 

57. 

100  gal. 

16. 

45  mi. 

37. 

8hr. 

58. 

8Jlb. 

17. 

12. 

38. 

123  and  123. 

59. 

75. 

18. 

375  T. 

39. 

756.86967. 

60. 

486  sq.  in.. 

19. 

$10,890. 

40. 

424.26+  ft. 

729  cu.  in. 

20. 

$5.25. 

41. 

3.71. 

61. 

0.0220+  A. 

21. 

$80. 

42. 

45  ft. 

62. 

2i. 

30 


ANSWERS 


63.  154sq.  in.,  98sq.  in.   76.   li  da. 

64.  l,178,57.1f  ft.  77.  3  hr.  30  min. 

65.  8  ft.  3  in.  78.  4%. 

66.  98  da.  79.   1,456,700  bbl. 

67.  760.  80,  2  hr.  2^  min. 

68.  13JyVTrmi.  81.   13,600  1b. 

69.  $24,  $40,  $48.  82.  45  mi. 

70.  45  A.  83.  11.175-  mi. 

71.  9.  84.  $85.50. 

72.  6  da.  85.  $10.15. 

73.  $106.64.  86.   IJ. 

74.  46.58+  ft.  87.  336  bu. 
76.  2.3535  +  .                       88.   +  174, 

101.  8.085  bbl.,  26.565  bbl. 

102.  34cu.ft.,  17cu.  ft.,  102cu.ft.       ^ 

103.  10ibbl.,6f^cu.  yd. 

104.  191,666|. 

105.  750  yd.,  16f  min. 

106.  $1.25,  $1.60,  $2.20. 

107.  10,800  ft. 

108.  J  hr.,  1 J  mi.  from  first  place. 

109.  $17.90. 

110.  -^5  qt.,  3^0  qt.  ;  therefore  120'. 

If  qt.,  or  m  qt. 

121.  2  hr.  27  min.  lO^V  sec,  3  hr. 

122.  5  hr.  10  min.  54/j- sec,  5  hr.  43  min.  38y\  sec,  5  hr.  27  min.  163-^  sec 

123.  9  hr.  5  min.  27y\  sec,  9  hr.  27  min.  IG^^  sec 

124.  17  min.  30  sec.  p.m. 

125.  The  year  2878.  128.  $187.50,  $42.75. 

126.  1,418,000  bales.  129.  $148. 

127.  53i|%,  14iff%,  lblii%.  130.  $150,  $11.50. 
131.  $1,228  +  ,  $1.20,  $1.04,  $1.10,  $1.01,  $1.20,  $1.12,  $1.05. 


89.  2. 

90.  283,104. 

91.  $1700. 

92.  28,032,232.8  A. 

93.  1,860,012. 

94.  5wk. 

95.  8426.88  gal. 

96.  18/^%. 

97.  $1.49. 

98.  268,800. 

99.  4. 
100.   10  min. 

-  23,  +  7. 

111.  66  steps. 

112.  5077|T. 

113.  729,  162if|qt. 

114.  1,608,921.6  T. 

115.  $161,  $184. 

116.  $42,  $48,  $60. 

117.  $6. 

118.  51  ft.,  11,  7,  9. 

119.  1  hr.  5  min.  27y\  sec. 
4  hr.  21  min.  49^j  sec, 

7  hr.  38  min.  lO^f  sec 


-TT'nP     25     CENTS 

WIUU  BE   ASSESS^  ^^£       ^!^^E  FOURTH 

DAY     AND    TO     $l-0  ^^^_^____^ 

OVERDUE. 

DEC  291932     1      jan  31  1938 


.    a  iQ^      NOV    2  1939 
MAR    8  193* 

^^"^   <    1937\  MAR   5 1941 

SEP  22   10*5 


V^^^ 

NOV   181937 


l5JitV49<;l 


,/     .    /I    9W!ar'56j5 
fl.  1  P95S 


^     YB   (7246 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


